Using almost disjoint coding we prove the consistency of the existence of a definable ω-mad family of infinite subsets of ω together with.

Two sets are said to be almost disjoint if their intersection is finite. Almost disjoint subsets of [ω]ω and ωω have been studied for quite some time. In particular, the cardinal invariants \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{a}}$$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{a}_e}$$\end{document}, defined to be the minimum cardinality of a maximal infinite almost disjoint family of [ω]ω and ωω respectively, are known to be consistently less than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{c}}$$\end{document}. Here we examine analogs for functions in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^\omega}$$\end{document} and projections on l2, showing that they too can be consistently less than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{c}}$$\end{document}. (shrink)

We show that is consistent with the existence of a -definable wellorder of the reals and a -definable ω-mad subfamily of [ω]ω.

We show that the existence of a ${\Pi^1_1}$ -definable mad family is consistent with the existence of a ${\Delta^{1}_{3}}$ -definable well-order of the reals and ${\mathfrak{b}=\mathfrak{c}=\aleph_3}$.

We study the notion of [Formula: see text]-MAD families where [Formula: see text] is a Borel ideal on [Formula: see text]. We show that if [Formula: see text] is any finite or countably iterated Fubini product of the ideal of finite sets [Formula: see text], then there are no analytic infinite [Formula: see text]-MAD families, and assuming Projective Determinacy and Dependent Choice there are no infinite projective [Formula: see text]-MAD families; and under the full Axiom (...) of Determinacy [Formula: see text][Formula: see text] or under [Formula: see text] there are no infinite [Formula: see text]-mad families. Similar results are obtained in Solovay’s model. These results apply in particular to the ideal [Formula: see text], which corresponds to the classical notion of MAD families, as well as to the ideal [Formula: see text]. The proofs combine ideas from invariant descriptive set theory and forcing. (shrink)

Michel Foucault was the first to embed the roots of human sexuality in discipline and biopolitics, therefore revolutionizing our conception of sex and its relationship to society, economics, and culture. Yet over the past two decades, scholars have limited themselves to the study of Foucault's _History of Sexuality_, volume 1 paying lesser attention to his equally explosive _History of Madness_. In this earlier volume, Foucault recasts Western rationalism as a project that both produces and represses sexual deviants, calling out the (...) complicity of modern science and the exclusionary nature of family morality. By reclaiming these deft moves, Lynne Huffer teases out exciting new strands of Foucauldian thought. She then revisits the theorist's ethical work in light of these discoveries, divining an ethics of eros that sees sexuality as a lived experience we are repeatedly called on to remember. Throughout her study, Huffer weaves her own experiences together with Foucault's, sampling from unpublished interviews and other archived materials in order to intimately rework the problem of sexuality as a product of reason. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Lynn Huffer's Mad For Foucault:An Analysis of Historical Eros?Laura HengeholdMad for Foucault is a remarkably beautiful book balanced on the edges between the personal, the impersonal, and the public and reflected through Foucault's own struggles to establish those divides. Huffer's goal in Mad for Foucault is to draw scholarly attention to the emotional and ethical content of Foucault's writing, as well as to assess the risks of queer theory's (...) dependence on dialectics and psychoanalytic theory. Reading History of Sexuality I in light of History of Madness, she argues, renders the ethical aspects of Foucault's early project clear and reveals the continuity with his later work on ethics, putting the central concerns of queer theory in a different light. But this continuity is only visible through attention to the lyrical force resulting from tensions between these edges, which also separate genders and epochs, as if Las Meninas were to draw the viewer's gaze toward a fractured mirror rather than a sovereign one.The elements of History of Sexuality I that have been most important for the queer theorists Huffer engages are Foucault's attempt to date the shifts from a perception of sinful acts to a perception of homosexual personality types, and his warning that reifying such personality types as "identities" in hopes of liberation from heterosexist oppression continues to support the social mechanisms that identify personal truth with sexuality. Some (associated with Judith Butler) have tried to develop an account of agency that owes less to the exclusions of traditional moral and psychological theories but risks establishing its own hierarchies of psychic "health." Others (Lee Edelman is exemplary) [End Page 226] have also argued that the affects associated with these acts and identities, and possibly the ethical attitudes arising from these affects, are historical effects that must be bracketed in the name of resisting biopower (Huffer 2010, 94-95).Both groups, Huffer argues, have merely performed a dialectical reversal within the order of sexualities inherited from the nineteenth century, without appreciating Foucault's effort to cast the very terms of that order into question—above all, in History of Madness (Huffer 2010, 113-16). What is more disturbing, both sides have enlisted psychoanalysis on their behalf, although Foucault remained skeptical of psychoanalysis. In History of Madness (2006a), Foucault's skepticism was justified in the name of the affective attachments of queer life and his deeply felt fascination for the traces of a sexual hybridity almost erased from European history. For Huffer, the real question posed by both History of Sexuality I and History of Madness is not, as queer theorists might believe, "why sexuality became a moral issue" (and how might it cease to be one) but who was buried when the nineteenth-century medicalization of sexuality replaced erotic experience with explanations of sexual abnormalities (2010, 229). She reads Foucault's work as a meditation on the ethical tragedy presented by the scattered ashes of even "infamous men."Although there are many themes I could address, I will let my comments be guided by Huffer's reading of the explicit and implicit critique of psychoanalysis found in Foucault's work, and its relation to Foucault's ambivalent Kantianism (2010, 127-33, 134). This critique comes from several directions. First, throughout all his works, including Archeology of Knowledge, Foucault criticizes interpretive approaches to the historical record and to human speech. Practices such as "commentary" reduce the variety of events that can be perceived in the historical field and turn some into the content or meaning of others, which are thereby privileged metaphysically as "more real." Second, Foucault criticizes power relations forcing some to confess and to interpret the products of their own confession in terms of the meanings religious or medical authorities insist on finding there. From the seventeenth century through the present, such authorities have identified work and family-oriented behavior as "reasonable" and have forced those whose behavior does not fit those terms to understand themselves as deviations from that norm (Huffer 2010, 105, 107-108).Third, according to Huffer, Foucault subjects belief in the psyche as scientific object and focus of work on the self to historical analysis... (shrink)

An ordering (≤K) on maximal almost disjoint (MAD) families closely related to destructibility of MAD families by forcing is introduced and studied. It is shown that the order has antichains of size.

Let ${\cal I}$ be an ideal on ω. By cov${}_{}^{\rm{*}}$ we denote the least size of a family ${\cal B} \subseteq {\cal I}$ such that for every infinite $X \in {\cal I}$ there is $B \in {\cal B}$ for which $B\mathop \cap \nolimits X$ is infinite. We say that an AD family ${\cal A} \subseteq {\cal I}$ is a MAD family restricted to${\cal I}$ if for every infinite $X \in {\cal I}$ there is $A \in {\cal A}$ such that $|X\mathop (...) \cap \nolimits A| = \omega$. Let a$\left$ be the least size of an infinite MAD family restricted to ${\cal I}$. We prove that If $max${a,cov${}_{}^{\rm{*}}\}$ then a$\left = {\omega _1}$, and consequently, if ${\cal I}$ is tall and $\le {\omega _2}$ then a$\left = max$ {a,cov${}_{}^{\rm{*}}\}$. We use these results to prove that if c$\le {\omega _2}$ then o$= \overline o$ and that as$= max${a,non$\}$. We also analyze the problem whether it is consistent with the negation of CH that every AD family of size ω1 can be extended to a MAD family of size ω1. (shrink)

Let κ be a regular cardinal and P a partial ordering preserving the regularity of κ. If P is (κ-Baire and) of density κ, then there is a mad family on κ killed in all generic extensions (if and) only if below each p∈P there exists a κ-sized antichain. In this case a mad family on κ is killed (if and) only if there exists an injection from κ onto a dense subset of Ult(P) mapping the elements of onto nowhere (...) dense sets. If 2< κ =κ, then in each generic extension of V, in which κ is the minimal cardinal obtaining new subsets, some mad family on κ is killed or an independent subset of κ appears. Also, the κ-Suslin Hypothesis holds iff there exists a mad family on κ which is killed in each generic extension containing new subsets of κ and preserving P(λ) for λ<κ. (shrink)

This thesis divides naturally into two parts, each concerned with the extent to which the theory of $L$ can be changed by forcing.The first part focuses primarily on applying generic-absoluteness principles to how that definable sets of reals enjoy regularity properties. The work in Part I is joint with Itay Neeman and is adapted from our paper Happy and mad families in $L$, JSL, 2018. The project was motivated by questions about mad families, maximal families of infinite (...) subsets of $\omega $ of which any two have only finitely many members in common. We begin, in the spirit of Mathias, by establishing a strong Ramsey property for sets of reals in the Solovay model, giving a new proof of Törnquist’s theorem that there are no infinite mad families in the Solovay model.In Chapter 3 we stray from the main line of inquiry to briefly study a game-theoretic characterization of filters with the Baire Property.Neeman and Zapletal showed, assuming roughly the existence of a proper class of Woodin cardinals, that the boldface theory of $L$ cannot be changed by proper forcing. They call their result the Embedding Theorem, because they conclude that in fact there is an elementary embedding from the $L$ of the ground model to that of the proper forcing extension. With a view toward analyzing mad families under $\mathsf {AD}^+$ and in $L$ under large-cardinal hypotheses, in Chapter 4 we establish triangular versions of the Embedding Theorem. These are enough for us to use Mathias’s methods to show that there are no infinite mad families in $L$ under large cardinals and that $\mathsf {AD}^+$ implies that there are no infinite mad families. These are again corollaries of theorems about strong Ramsey properties under large-cardinal assumptions and $\mathsf {AD}^+$, respectively. Our first theorem improves the large-cardinal assumption under which Todorcevic established the nonexistence of infinite mad families in $L$. Part I concludes with Chapter 5, a short list of open questions.In the second part of the thesis, we undertake a finer analysis of the Embedding Theorem and its consistency strength. Schindler found that the the Embedding Theorem is consistent relative to much weaker assumptions than the existence of Woodin cardinals. He defined remarkable cardinals, which can exist even in L, and showed that the Embedding Theorem is equiconsistent with the existence of a remarkable cardinal. His theorem resembles a theorem of Harrington–Shelah and Kunen from the 1980s: the absoluteness of the theory of $L$ to ccc forcing extensions is equiconsistent with a weakly compact cardinal. Joint with Itay Neeman, we improve Schindler’s theorem by showing that absoluteness for $\sigma $ -closed $\ast $ ccc posets—instead of the larger class of proper posets—implies the remarkability of $\aleph _1^V$ in L. This requires a fundamental change in the proof, since Schindler’s lower-bound argument uses Jensen’s reshaping forcing, which, though proper, need not be $\sigma $ -closed $\ast $ ccc in that context. Our proof bears more resemblance to that of Harrington–Shelah than to Schindler’s.The proof of Theorem 6.2 splits naturally into two arguments. In Chapter 7 we extend the Harrington–Shelah method of coding reals into a specializing function to allow for trees with uncountable levels that may not belong to L. This culminates in Theorem 7.4, which asserts that if there are $X\subseteq \omega _1$ and a tree $T\subseteq \omega _1$ of height $\omega _1$ such that X is codable along T, then $L$ -absoluteness for ccc posets must fail.We complete the argument in Chapter 8, where we show that if in any $\sigma $ -closed extension of V there is no $X\subseteq \omega _1$ codable along a tree T, then $\aleph _1^V$ must be remarkable in L.In Chapter 9 we review Schindler’s proof of generic absoluteness from a remarkable cardinal to show that the argument gives a level-by-level upper bound: a strongly $\lambda ^+$ -remarkable cardinal is enough to get $L$ -absoluteness for $\lambda $ -linked proper posets.Chapter 10 is devoted to partially reversing the level-by-level upper bound of Chapter 9. Adapting the methods of Neeman, Hierarchies of forcing axioms II, we are able to show that $L$ -absoluteness for $\left |\mathbf {R}\right |\cdot \left |\lambda \right |$ -linked posets implies that the interval $[\aleph _1^V,\lambda ]$ is $\Sigma ^2_1$ -remarkable in L.prepared by Zach Norwood.E-mail: [email protected]. (shrink)

We show that Hechler’s forcings for adding a tower and for adding a mad family can be represented as finite support iterations of Mathias forcings with respect to filters and that these filters are $${\mathcal {B}}$$ B -Canjar for any countably directed unbounded family $${\mathcal {B}}$$ B of the ground model. In particular, they preserve the unboundedness of any unbounded scale of the ground model. Moreover, we show that $${\mathfrak {b}}=\omega _1$$ b = ω 1 in every extension by the (...) above forcing notions. (shrink)

In set theory without the Axiom of Choice ( $\mathsf {AC}$ ), we investigate the open problem of the deductive strength of statements which concern the existence of almost disjoint and maximal almost disjoint (MAD) families of infinite-dimensional subspaces of a given infinite-dimensional vector space, as well as the extension of almost disjoint families in infinite-dimensional vector spaces to MAD families.

We continue with the study of the Katětov order on MAD families. We prove that Katětov maximal MAD families exist under $\mathfrak {b=c}$ and that there are no Katětov-top MAD families assuming $\mathfrak {s\leq b}.$ This improves previously known results from the literature. We also answer a problem form Arciga, Hrušák, and Martínez regarding Katětov maximal MAD families.

Let κ < λ be regular uncountable cardinals. Using a finite support iteration (in fact a matrix iteration) of ccc posets we obtain the consistency of b = a = κ < s = λ. If μ is a measurable cardinal and μ < κ < λ, then using similar techniques we obtain the consistency of b = κ < a = s = λ.

In this survey paper we collect several known results on destroying tall ideals on countable sets and maximal almost disjoint families with forcing. In most cases we provide streamlined proofs of the presented results. The paper contains results of many authors as well as a preview of results of a forthcoming paper of Brendle, Guzmán, Hrušák, and Raghavan.

We prove that Martin’s Axiom implies the existence of a Cohen-indestructible mad family such that the Mathias forcing associated to its filter adds dominating reals, while \ is consistent with the negation of this statement as witnessed by the Laver model for the consistency of Borel’s conjecture.

The main topics of this thesis are cardinal invariants, P -points and MAD families. Cardinal invariants of the continuum are cardinal numbers that are bigger than $\aleph _{0}$ and smaller or equal than $\mathfrak {c}.$ Of course, they are only interesting when they have some combinatorial or topological definition. An almost disjoint family is a family of infinite subsets of $\omega $ such that the intersection of any two of its elements is finite. A MAD family is a maximal (...) almost disjoint family. An ultrafilter $\mathcal {U}$ on $\omega $ is called a P-point if every countable $\mathcal {B\subseteq U}$ there is $X\in $ $\mathcal {U}$ such that $X\setminus B$ is finite for every $B\in \mathcal {B}.$ This kind of ultrafilters has been extensively studied, however there is still a large number of open questions about them.In the preliminaries we recall the principal properties of filters, ultrafilters, ideals, MAD families and cardinal invariants of the continuum. We present the construction of Shelah, Mildenberger, Raghavan, and Steprāns of a completely separable MAD family under $\mathfrak {s\leq a}.$ None of the results in this chapter are due to the author.The second chapter is dedicated to a principle of Sierpiński. The principle $\left $ of Sierpiński is the following statement: There is a family of functions $\left \{ \varphi _{n}:\omega _{1}\longrightarrow \omega _{1}\mid n\in \omega \right \} $ such that for every $I\in \left [ \omega _{1}\right ] ^{\omega _{1}}$ there is $n\in \omega $ for which $\varphi _{n}\left [ I\right ] =\omega _{1}.$ This principle was recently studied by Arnie Miller. He showed that this principle is equivalent to the following statement: There is a set $X=\left \{ f_{\alpha }\mid \alpha \alpha $ then $f_{\beta }\cap g$ is infinite. Miller showed that the principle of Sierpiński implies that non $\left =\omega _{1}.$ He asked if the converse was true, i.e., does non $\left =\omega _{1}$ imply the principle $\left $ of Sierpiński? We answer his question affirmatively. In other words, we show that non $\left =\omega _{1}$ is enough to construct an $\mathcal {IE}$ -Luzin set. It is not hard to see that the $\mathcal {IE}$ -Luzin set we constructed is meager. This is no coincidence, because with the aid of an inaccessible cardinal, we construct a model where non $\left =\omega _{1}$ and every $\mathcal {IE}$ -Luzin set is meager.The third chapter is dedicated to a conjecture of Hrušák. Michael Hrušák conjectured the following: Every Borel cardinal invariant is either at most non $\left $ or at least cov $\left $. Although the veracity of this conjecture is still an open problem, we were able to obtain some partial results: The conjecture is false for “Borel invariants of $\omega _{1}^{\omega }$ ” nevertheless, it is true for a large class of definable invariants. This is part of a joint work with Michael Hrušák and Jindřich Zapletal.In the fourth chapter we present a survey on destructibility of ideals and MAD families. We prove several classic theorems, but we also prove some new results. For example, we show that every almost disjoint family of size less than $\mathfrak {c}$ can be extended to a Cohen indestructible MAD family is equivalent to $\mathfrak {b=c}$. A MAD family $\mathcal {A}$ is Shelah–Steprāns if for every $X\subseteq \left [ \omega \right ] ^{<\omega }\setminus \left \{ \emptyset \right \} $ either there is $A\in \mathcal {I}\left $ such that $s\cap A\neq \emptyset $ for every $s\in X$ or there is $B\in \mathcal {I}\left $ that contains infinitely many elements of X $ denotes the ideal generated by $\mathcal {A}$ ). This concept was introduced by Raghavan which is connected to the notion of “strongly separable” introduced by Shelah and Steprāns. We prove that Shelah–Steprāns MAD families have very strong indestructibility properties: Shelah–Steprāns MAD families are indestructible for “many” definable forcings that does not add dominating reals. According to the author’s best knowledge, this is the strongest notion that has been considered in the literature so far. In spite of their strong indestructibility, Shelah–Steprāns MAD families can be destroyed by a ccc forcing that does not add unsplit or dominating reals. We also consider some strong combinatorial properties of MAD families and show the relationships between them.The fifth chapter is one of the most important chapters in the thesis. A MAD family $\mathcal {A}$ is called $+$ -Ramsey if every tree that branches into $\mathcal {I}\left $ -positive sets has an $\mathcal {I}\left $ -positive branch. Michael Hrušák’s first published question is the following: Is there a $+$ -Ramsey MAD family? It was previously known that such families can consistently exist. However, there was no construction of such families using only the axioms of ZFC. We solve this problem by constructing such a family without any extra assumptions.In the fourth and fifth chapters, we introduce several notions of MAD families, in the sixth chapter we prove several implications and non implications between them. We construct several MAD families with different properties.In the seventh chapter we build models without P -points. We show that there are no P -points after adding Silver reals either iteratively or by the side by side product. These results have some important consequences: The first one is that is its possible to get rid of P -points using only definable forcings. This answers a question of Michael Hrušák. We can also use our results to build models with no P -points and with arbitrarily large continuum, which was also an open question. These results were obtained with David Chodounský.prepared by Osvaldo Guzmán GonzálezE-mail : [email protected] : https://arxiv.org/abs/1810.09680. (shrink)

We show in ZFC that the existence of completely separable maximal almost disjoint families of subsets of $\omega $ implies that the modal logic $\mathbf {S4.1.2}$ is complete with respect to the Čech–Stone compactification of the natural numbers, the space $\beta \omega $. In the same fashion we prove that the modal logic $\mathbf {S4}$ is complete with respect to the space $\omega ^*=\beta \omega \setminus \omega $. This improves the results of G. Bezhanishvili and J. Harding in [4], (...) where the authors prove these theorems under stronger assumptions. Our proof is also somewhat simpler. (shrink)

We show in ZFC that the existence of completely separable maximal almost disjoint families of subsets of $\omega $ implies that the modal logic $\mathbf {S4.1.2}$ is complete with respect to the Čech–Stone compactification of the natural numbers, the space $\beta \omega $. In the same fashion we prove that the modal logic $\mathbf {S4}$ is complete with respect to the space $\omega ^*=\beta \omega \setminus \omega $. This improves the results of G. Bezhanishvili and J. Harding in [4], (...) where the authors prove these theorems under stronger assumptions. Our proof is also somewhat simpler. (shrink)

We show the consistency of ${\frak o} <{\frak d}$ where ${\frak o}$ is the size of the smallest off-branch family, and ${\frak d}$ is as usual the dominating number. We also prove the consistency of ${\frak b} < {\frak a}$ with large continuum. Here, ${\frak b}$ is the unbounding number, and ${\frak a}$ is the almost disjointness number.

The rural-migrant protagonist in Knut Hamsun’s Hunger fails to adapt to the urban environment because the moral algorithm that informs his collaborative choices is unfit for the city. He often responds poorly when overwhelmed by pride, shame, or other sensations that he struggles to make sense of. Such emotions are hypothesized to be neuro­computational adaptations crafted by natural selection to help us get ahead as collabora­tors. But with societal transformation, these feelings can become a poor match for a new reality. (...) Reprogramming oneself can be challenging; Hunger’s protagonist must suffer months of emotional and physical pain before he adapts. His journey, and Hamsun’s mod­ernist project, can be illuminated by recent research on status management and morality as cooperation. As literature, Hunger could fulfill several adaptive functions by mapping mor­als for urban pro-sociality at a time of great disruption. Similar moral adaptation could become necessary in our present era, too. (shrink)

Let A[ω]ω be a maximal almost disjoint family and assume P is a forcing notion. Say A is P-indestructible if A is still maximal in any P-generic extension. We investigate P-indestructibility for several classical forcing notions P. In particular, we provide a combinatorial characterization of P-indestructibility and, assuming a fragment of MA, we construct maximal almost disjoint families which are P-indestructible yet Q-destructible for several pairs of forcing notions . We close with a detailed investigation of iterated Sacks indestructibility.

Artificial intelligence is likely to undermine the anthropocentrism of humanism, the master narrative that undergirds the modern world. Humanity will need a new story to structure our beliefs and cooperation around. As different regions explore posthumanist alternatives through fiction, they bring with them distinct traditions of thought. The Swedish TV series _Real Humans_ (2012–2014) and its British remake, _Humans_ (2015–2018), dramatize the challenge of freeing oneself from cultural presumptions. When negotiating personhood with humanoid robots, the Swedish protagonist family presupposes a (...) social-democratic ethos, which is a trace of Scandinavian humanism that carries into the family’s posthumanist beliefs. Using Heideggerian and related perspectives, I analyze these series to make a case for a _dataist_ ontology with potential to re-enchant the modern world and bring forth a new epoch of being. Such a master narrative of _algorithmic universality_ could be facilitated by a new level of interconnectedness made possible by AI. This ontology fulfills the requirements of Robbins and Horta (Introduction, Cosmopolitanisms. New York University Press, New York, pp 1–17, 2017) who call for a cosmopolitanism of inclusivity with room for overlapping conceptions to remedy our present era’s international dysfunction. The Swedish and British TV series suggest that even if humanity’s uniting around a dataist master narrative were to be driven by intercultural competition, the decisive choice might be out of human hands. Paradoxically, such disempowering in terms of agency is portrayed as necessary for human _re-enchantment_. (shrink)

We show that the non-existence of mad families is equiconsistent with \, answering an old question of Mathias. We also consider the above result in the general context of maximal independent sets in Borel graphs, and we construct a Borel graph G such that \ “there is no maximal independent set in G” is equiconsistent with \ “there exists an inaccessible cardinal”.

Starting from a model with a Laver-indestructible supercompact cardinal $$\kappa $$, we construct a model of $$ZF+DC_{\kappa }$$ where there are no $$\kappa $$ -mad families.

Collected articles on Islamic Ethics, doctrines. and Ahmadiyya family.

This essay is part of a larger project in which I construct a new, historically-informed, social justice-centered philosophy of dance, centered on four central phenomenological constructs, or “Moves.” This essay in particular is about the fourth Move, “resilience.” More specifically, I explore how Judith Butler engages with the etymological aspects of this word, suggesting that resilience involves a productive form of madness and a healthy form of compulsion, respectively. I then conclude by showing how “resilience” can be used in the (...) analysis of various Wittgensteinian “families” of dance, which in turn could facilitate positive educational changes in philosophy, dance and society, with particular efficacy on the axis of gender. In brief, by teaching a conception of strength as vulnerability (instead of machismo’s view of strength as apathetic “toughness”), a pedagogy of dancing resilience provides additional support for feminists (including Anzaldúa, Haraway, Butler and Concepción) who advocate a cautious openness toward seemingly-unlikely resources and allies (including analytic methodologies, Machiavellian politics, and the discourses of the natural sciences). (shrink)

Physical and emotional intimacy between humans and robots may become commonplace over the next decades, as technology improves at a rapid rate. This development provides new questions pertaining to how people perceive robots designed for different kinds of intimacy, both as companions and potentially as competitors. We performed an randomized experiment where participants read of either a robot that could only perform sexual acts, or only engage in non-sexual platonic love relationships. The results of the current study show that females (...) have less positive views of robots, and especially of sex robots, compared to men. Contrary to the expectation rooted in evolutionary psychology, females expected to feel more jealousy if their partner got a sex robot, rather than a platonic love robot. The results further suggests that people project their own feelings about robots onto their partner, erroneously expecting their partner to react as they would to the thought of ones’ partner having a robot. (shrink)

On the rights of husband and wife according to Islamic teachings.

In “Cogito and the History of Madness,” Derrida maintains that crisis is endemic to philosophy rather than being, as Husserl forcefully argued, a temporary condition that can and must be overcome through the resources of reason. A reflection on the place of madness in Descartes's Meditations serves as the point of departure for demonstrating that Derrida has done an injustice to philosophy; and a comparison of Derrida's views with the thought of Husserl, Heidegger, and Nietzsche reveals that Derrida's position in (...) “Cogito and the History of Madness” entails a sacrifice of the notion of responsibility that lies at the center of meaningful historical action. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Nietzsche and Rée: A Star FriendshipDaw-Nay N. R. Evans Jr.Robin Small. Nietzsche and Rée: A Star Friendship. Oxford: Clarendon Press, 2005. Pp. xxiv + 247. Cloth, $45.00.Nietzsche attracts a wide range of scholarly enthusiasts. There are those who take Nietzsche seriously as a philosopher and study his works for their own sake, while others seek to mine his works for philosophical gold to determine what he might have (...) to offer their particular area of specialization (and sometimes these objectives overlap). On the other hand, there are those who seek to sensationalize Nietzsche by making him out to be a caricature or buffoon of sorts—far less deserving of the kind of seriousness we reserve for other figures such as Descartes or Kant. Instead, Nietzsche's philosophical legacy is colored by his ill health, alleged homosexuality, or "madness." Some recent biographies have only perpetuated the caricature. Fortunately, Small's book is not one of them.Small aims to explain the philosophical relationship between Nietzsche and Rée. Nietzsche's background is well known, while Rée's life has received only slight attention from scholars. Although he did not self-identify as Jewish, Rée was born into a wealthy Jewish family, which afforded him the luxury of attending several different German universities. After studying law, psychology, and physiology, he finally settled on philosophy. By the time Rée met Nietzsche, he had already defended a dissertation on Aristotle's ethics and published his first book, Psychological Observations, in 1875.Throughout the book, Small subtly fuses the personal with the philosophical without weakening the philosophical substance of Nietzsche's or Rée's ideas. In explaining Rée's influence on Nietzsche during the seven years of their friendship, Small accomplishes several objectives.First and foremost, Small illuminates the development of Nietzsche's thought from 1875 until 1882. It was during these years that Nietzsche published Human, All Too Human (1878; the first supplement to the book was published in 1879 and the second in 1880), Daybreak (1881), and The Gay Science (1882). More importantly, Small demonstrates the nexus between these works and Rée's Psychological Observations (1875) and The Origin of Moral Sensations.During the winter of 1876–77, Nietzsche and Rée lived together. At this time Nietzsche began writing Human, All Too Human, while Rée wrote The Origin of Moral Sensations. Nietzsche turned to Rée's Psychological Observations for headings for his own Human, All Too Human. Thus, "'On Religious Things' became 'The Religious Life,' while 'On Woman, Love and Marriage' became 'Woman and Child'" (28). As Nietzsche continued work on Human, All Too Human, Rée's The Origin of Moral Sensations was published and Nietzsche drew inspiration from this book as well. In section 40 of The Wanderer and His Shadow (the second supplement to Human, All Too Human), Nietzsche provides an abbreviated version of the core argument of that work, namely that the move away from utility and towards socially accepted norms as the determining factor in behavior is what led to morality. For these reasons, it is no surprise that Nietzsche referred to the "Rée-ness" of his work, and dubbed books like Human, All Too Human as "Réealism" (x, 33, 65). [End Page 672]Second, Small makes clear the shared philosophical sympathies that made their relationship possible. Their mutual admiration for Schopenhauer, denial of free will, skepticism about morality and metaphysics, and adherence to philosophical naturalism created a friendship that nurtured their philosophical development generally and their philosophical projects more specifically.Third, Small sheds light on how Nietzsche integrated Rée's aphoristic style into his own philosophical writings. This is helpful because it contextualizes Nietzsche's writing style during the time when his strict preoccupation with philological matters had ended and he began exhibiting contempt for morality and extolling the virtues of scientific knowledge.Fourth, Small discusses Nietzsche's break with Rée, the central tension of which he locates in Nietzsche's willingness to move beyond Rée's merely descriptive approach to moral phenomena towards a life-affirming philosophy. To be sure, Nietzsche envisioned Human, All Too... (shrink)

A maximal almost disjoint (mad) family $\mathscr{A} \subseteq [\omega]^\omega$ is Cohen-stable if and only if it remains maximal in any Cohen generic extension. Otherwise it is Cohen-unstable. It is shown that a mad family, A, is Cohen-unstable if and only if there is a bijection G from ω to the rationals such that the sets G[A], A ∈A are nowhere dense. An ℵ 0 -mad family, A, is a mad family with the property that given any countable family $\mathscr{B} \subset (...) [\omega]^\omega$ such that each element of B meets infinitely many elements of A in an infinite set there is an element of A meeting each element of B in an infinite set. It is shown that Cohen-stable mad families exist if and only if there exist ℵ 0 -mad families. Either of the conditions b = c or $\mathfrak{a} ) implies that there exist Cohen-stable mad families. Similar results are obtained for splitting families. For example, a splitting family, S, is Cohen-unstable if and only if there is a bijection G from ω to the rationals such that the boundaries of the sets G[S], S ∈S are nowhere dense. Also, Cohen-stable splitting families of cardinality ≤ κ exist if and only if ℵ 0 -splitting families of cardinality ≤ κ exist. (shrink)

L’épreuve projective intitulée « spatiographie projective familiale » a pour objectif de comprendre l’image inconsciente du corps familial à travers l’analyse du dessin groupal de la « maison de rêve ». Par cette méthodologie, les auteurs peuvent établir un diagnostic de la structure des liens inconscients de la famille et en faire un objet médiateur pour la prise en charge psychothérapique et une épreuve projective groupale familiale pour le diagnostic. Le dessin de la « maison de rêve (...) » est un outil original qui investigue les dimensions diachronique et synchronique permettant une approche complète de la structuration de l’image du corps familial. (shrink)

We consider maximal almost disjoint families of block subspaces of countable vector spaces, focusing on questions of their size and definability. We prove that the minimum infinite cardinality of such a family cannot be decided in ZFC and that the “spectrum” of cardinalities of mad families of subspaces can be made arbitrarily large, in analogy to results for mad families on ω. We apply the author’s local Ramsey theory for vector spaces [32] to give partial results concerning (...) their definability. (shrink)

Classifying Madness (Springer, 2005) concerns philosophical problems with the Diagnostic and Statistical Manual of Mental Disorders, more commonly known as the D.S.M. The D.S.M. is published by the American Psychiatric Association and aims to list and describe all mental disorders. The first half of Classifying Madness asks whether the project of constructing a classification of mental disorders that reflects natural distinctions makes sense. Chapters examine the nature of mental illness, and also consider whether mental disorders fall into natural kinds. The (...) second half of the book addresses epistemic worries. Even supposing a natural classification system to be possible in principle, there may be reasons to be suspicious of the categories included in the D.S.M. I examine the extent to which the D.S.M. depends on psychiatric theory, and look at how it has been shaped by social and financial factors. I aim to be critical of the D.S.M. without being antagonistic towards it. Ultimately, however, I am forced to conclude that although the D.S.M. is of immense practical importance, it is unlikely to come to reflect the natural structure of mental disorders. (shrink)

Assuming the existence of a supercompact cardinal, we construct a model where, for some uncountable regular cardinal κ, there are no κ‐mad families.

Present research proposes the application of unsupervised and supervised machine-learning techniques to characterize Android malware families. More precisely, a novel unsupervised neural-projection method for dimensionality-reduction, namely, Beta Hebbian Learning, is applied to visually analyze such malware. Additionally, well-known supervised Decision Trees are also applied for the first time in order to improve characterization of such families and compare the original features that are identified as the most important ones. The proposed techniques are validated when facing real-life Android malware (...) data by means of the well-known and publicly available Malgenome dataset. Obtained results support the proposed approach, confirming the validity of BHL and DTs to gain deep knowledge on Android malware. (shrink)

SummaryThis report describes a family planning KAP survey conducted in 2000 households in rural Ghana between April and October, 1972, as one of the Danfa Project’s baseline studies. Subsequent re-surveys were done in 1975 and 1977 to assess changes related to project health education and family planning programmes.Reported knowledge about family planning was three times that reported in previous studies in rural Ghana. About 70% of the respondents approve of family planning, but most want a large family, with over six (...) children. At all ages, males wanted two or three more children than did women.The current 3% population growth rate in Ghana may increase due to continued early age of marriage, the rising size of the reproductive age group and improved pregnancy outcome.Although the expected relationships between knowledge and use of family planning and age and education were present, these differentials were typically only 10–15%. In the project area it appears that women will be most important in making the decision to practise family planning, although motivation of males is being stressed.Most villagers hear about family planning through informal, word-of-mouth channels with relatively little use of news media, family planning workers or clinic health personnel. To improve the practice of family planning, village-based health educators are working with volunteers including traditional birth attendants, community leaders, teachers and church groups. (shrink)