We prove a partition theorem for analytic sets, namely, if X is an analytic set in a Polish space and [X]n = K0 ∪ K1 with K0 open in the relative topology, and the partition satisfies a finitary condition, then either there is a perfect K0-homogeneous subset or X is a countable union of K1-homogeneous subsets. We also prove a partition theorem for analytic sets in the three-dimensional case. Finally, we give some applications of the theorems.

We discuss a dual of the Open Coloring Axiom introduced by Abraham et al. [U. Abraham, M. Rubin, S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of 1-dense real order types, Ann. Pure Appl. Logic 29 123–206] and show that it follows from a statement about continuous colorings on Polish spaces that is known to be consistent. We mention some consequences of the new axiom and show that implies that all cardinal (...) invariants in Cichoń’s diagram are at least 2. (shrink)

Let ⪯R be the preorder of embeddability between countable linear orders colored with elements of Rado's partial order . We show that ⪯R has fairly high complexity with respect to Borel reducibility , although its exact classification remains open.

We show that the Abraham–Rubin–Shelah Open Coloring Axiom is consistent with a large continuum, in particular, consistent with [Formula: see text]. This answers one of the main open questions from [U. Abraham, M. Rubin and S. Shelah, On the consistency of some partition theorems for continuous colorings, and the structure of [Formula: see text]-dense real order types, Ann. Pure Appl. Logic 325(29) (1985) 123–206]. As in [U. Abraham, M. Rubin and S. Shelah, On the consistency of some (...) partition theorems for continuous colorings, and the structure of [Formula: see text]-dense real order types, Ann. Pure Appl. Logic 325(29) (1985) 123–206], we need to construct names for the so-called preassignments of colors in order to add the necessary homogeneous sets. However, the known constructions of preassignments (ours in particular) only work assuming the [Formula: see text]. In order to address this difficulty, we show how to construct such names with very strong symmetry conditions. This symmetry allows us to combine them in many different ways, using a new type of poset called a partition product. Partition products may be thought of as a restricted memory iteration with stringent isomorphism and coherent-overlap conditions on the memories. We finally construct, in [Formula: see text], the partition product which gives us a model of [Formula: see text] in which [Formula: see text]. (shrink)

ABSTRACT There are forms of discriminations that are not defensible, and unjustified discriminations manifest in different forms. One such manifestation is racism, which involves the use of morally arbitrary natural and moral constituents (characteristics, abilities, qualities) to demarcate racial or ethnic groups and consequently designate some groups as superior and others as inferior. In this article, I discuss one form of racism (intellectual racism), namely, racism in relation to color, as a way of highlighting how the notion of superiority and (...) inferiority of racial or ethnic groups (Caucasian and Africans) play out in the intellectual landscape and discourse. Ultimately, my motivations are threefold: one, to signify and engage with some views of racial coloring and color eliminativism; two, to make and extend the position that color eliminativism is not defensible; and three, to highlight and emphasize the claim that given the notion of a “one-colored humanity,” racial groups ought not to be classified as superior or inferior. (shrink)

We introduce the relation of almost-reduction in an arbitrary topological Ramsey space ℛ as a generalization of the relation of almost-inclusion on ℕ[∞]. This leads us to a type of ultrafilter [MATHEMATICAL SCRIPT CAPITAL U] ⊆ ℛ which corresponds to the well-known notion of selective ultrafilter on ℕ. The relationship turns out to be rather exact in the sense that it permits us to lift several well-known facts about selective ultrafilters on ℕ and the Ellentuck space ℕ[∞] to the ultrafilter (...) [MATHEMATICAL SCRIPT CAPITAL U] and the Ramsey space ℛ. For example, we prove that the open coloring axiom holds on L [[MATHEMATICAL SCRIPT CAPITAL U]], extending therefore the result from [3] which gives the same conclusion for the Ramsey space ℕ[∞]. (shrink)

We show that bounded forcing axioms are consistent with the existence of -gaps and thus do not imply the Open Coloring Axiom. They are also consistent with Jensen's combinatorial principles for L at the level ω2, and therefore with the existence of an ω2-Suslin tree. We also show that the axiom we call BMM3 implies 21=2, as well as a stationary reflection principle which has many of the consequences of Martin's Maximum for objects of size 2. Finally, we (...) give an example of a so-called boldface bounded forcing axiom implying 20=2. (shrink)

Given a graph G whose set of vertices is a Polish space X, the weak Borel chromatic number of G is the least size of a family of pairwise disjoint G -independent Borel sets that covers all of X. Here a set of vertices of a graph G is independent if no two vertices in the set are connected by an edge.We show that it is consistent with an arbitrarily large size of the continuum that every closed graph on a (...) Polish space either has a perfect clique or has a weak Borel chromatic number of at most ℵ1. We observe that some weak version of Todorcevic's Open Coloring Axiom for closed colorings follows from MA.Slightly weaker results hold for Fσ-graphs. In particular, it is consistent with an arbitrarily large size of the continuum that every locally countable Fσ-graph has a Borel chromatic number of at most ℵ1.We refute various reasonable generalizations of these results to hypergraphs. (shrink)

The purpose of this communication is to survey a theory of liftings, as developed in author's thesis. The first result in this area was Shelah's construction of a model of set theory in which every automorphism of P/ Fin, where Fin is the ideal of finite sets, is trivial, or inother words, it is induced by a function mapping integers into integers. Soon afterwards, Velickovic, was able to extract from Shelah's argument the fact that every automorphism of P/ Fin with (...) a Baire-measurable lifting has to be trivial. This, for instance, implies that in Solovay's model all automorphisms are trivial. Later on, an axiomatic approach was adopted and Shelah's conclusion was drawn first from the Proper Forcing Axiom and then from the milder Open Coloring Axiom and Martin's Axiom. Both shifts from the quotient P/ Fin to quotients over more general ideals P/I and from automorphisms to arbitrary ho-momorphisms were made by Just in a series of papers, motivated by some problems in algebra and topology. (shrink)

It is well known that the appearance of food, particularly its color, can influence flavor perception and identification. However, food studies involving the manipulation of product color face inevitable limitations, from extrinsic flavors introduced by food coloring to the cost in development time and resources in order to produce different product variants. One solution lies in modern virtual reality technology, which has become increasingly accessible, sophisticated, and widespread over the past years. In the present study, we investigated whether making (...) a coffee look milkier in a VR environment can alter its perceived flavor and liking. Thirty-two United Kingdom consumers were given four samples of black cold brew coffee at 4 and 8% sucrose concentration. They wore VR headsets throughout the study and viewed the same coffee in a virtual setting. The color of the beverage was manipulated in VR, such that participants saw either a dark brown or light brown liquid as they sipped the coffee. A full factorial design was used so that each participant tasted each sweetness x color combination, Participants reported sweetness, creaminess, and liking for each sample. Results revealed that beverage color as viewed in VR significantly influenced perceived creaminess, with the light brown coffee rated to be creamier than dark brown coffee. However, beverage color did not influence perceived sweetness or liking. The present study supports the role of VR as a means of conducting food perception studies, either to gain a better understanding of multisensory integration, or, from an industry perspective, to enable rapid product testing when it may be time-intensive or costly to produce the same range of products in the real-world. Furthermore, it opens potential future opportunities for VR to promote healthy eating behavior by manipulating the visual appearance of foods. (shrink)

The thin set theorem for n-tuples and k colors states that every k-coloring of $[\mathbb {N}]^n$ admits an infinite set of integers H such that $[H]^n$ avoids at least one color. In this paper, we study the combinatorial weakness of the thin set theorem in reverse mathematics by proving neither $\operatorname {\mathrm {\sf {TS}}}^n_k$, nor the free set theorem imply the Erdős–Moser theorem whenever k is sufficiently large. Given a problem $\mathsf {P}$, a computable instance of $\mathsf {P}$ is (...) universal iff its solution computes a solution of any other computable $\mathsf {P}$ -instance. It has been established that most of Ramsey-type problems do not have a universal instance, but the case of Erdős–Moser theorem remained open so far. We prove that Erdős–Moser theorem does not admit a universal instance. (shrink)

Studies to neutrosophic graphs happens to be not only innovative and interesting, but gives a new dimension to graph theory. The classic coloring of edge problem happens to give various results. Neutrosophic tree will certainly find lots of applications in data mining when certain levels of indeterminacy is involved in the problem. Several open problems are suggested.

In this paper we study the automorphism groups of countable arithmetically saturated models of Peano Arithmetic. The automorphism groups of such structures form a rich class of permutation groups. When studying the automorphism group of a model, one is interested to what extent a model is recoverable from its automorphism group. Kossak-Schmerl [12] show that ifMis a countable, arithmetically saturated model of Peano Arithmetic, then Aut(M) codes SSy(M). Using that result they prove:Let M1. M2be countable arithmetically saturated models of Peano (...) Arithmetic such that Aut(M1)≅ Aut(M2).ThenSSy(M1) = SSy(M2).We show that ifMis a countable arithmetically saturated of Peano Arithmetic, then Aut(M) can recognize if some maximal open subgroup is a stabilizer of a nonstandard element, which is smaller than any nonstandard definable element. That fact is used to show the main theorem:Let M1,M2be countable arithmetically saturated models of Peano Arithmetic such thatAut(M1) ≅ Aut(M2).Then for every n<ωHere RT2nis Infinite Ramsey's Theorem stating that every 2-coloring of [ω]nhas an infinite homogeneous set. Theorem 0.2 shows that for models of a false arithmetic the converse of Kossak-Schmerl Theorem 0.1 is not true. Using the results of Reverse Mathematics we obtain the following corollary:There exist four countable arithmetically saturated models of Peano Arithmetic such that they have the same standard system but their automorphism groups are pairwise non-isomorphic. (shrink)

Hindman’s Theorem says that every finite coloring of the positive natural numbers has a monochromatic set of finite sums. Ramsey algebras, recently introduced, are structures that satisfy an analogue of Hindman’s Theorem. It is an open problem posed by Carlson whether every Ramsey algebra has an idempotent ultrafilter. This paper develops a general framework to study idempotent ultrafilters. Under certain countable setting, the main result roughly says that every nondegenerate Ramsey algebra has a nonprincipal idempotent ultrafilter in some (...) nontrivial countable field of sets. This amounts to a positive result that addresses Carlson’s question in some way. (shrink)

This paper introduces a new Ehrenfeucht-Fraïssé type game that is played on two classes of models rather than just two models. This game extends and generalizes the known Ajtai-Fagin game to the case when there are several alternating moves played in different models. The game allows Duplicator to delay her choices of the models till the very end of the game, making it easier for her to win. This adds on the toolkit of winning strategies for Duplicator in Ehrenfeucht-Fraïssé type (...) games and opens up new methods for tackling some open problems in descriptive complexity theory. As an application of the class game, it is shown that, if m is a power of a prime, then first order logic augmented with function quantifiers F1n of arity 1 and height n < m can not express that the size of the model is divisible by m. This, together with some new expressibility results for Henkin quantifiers H1n gives some new separation results on the class of finite models among various F1n on one hand and between F1n and H1n on the other. Since function quantifiers involve a bounded type of second order existential quantifiers, the class game solves an open problem raised by Fagin, which asks for some inexpressibility result using a winning strategy by Duplicator in a game that involves more than one coloring round. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Prufrock's Question and Roquentin's AnswerWilliam IrwinThere could not be two more different literary figures than the right-wing, religious T. S. Eliot and the left-wing, atheistic Jean-Paul Sartre. Yet there are striking connections between their first major publications, The Love Song of J. Alfred Prufrock (1917) and Nausea (1938). Eliot was aware of and critical of Sartre, especially in the commentary on No Exit in The Cocktail Party, and, no (...) doubt, Sartre became aware of Eliot.1 But as far as can be gleaned, Sartre did not read Eliot's Prufrock, prior to the publication of Nausea, despite his connection to Adrienne Monnier, the French translator of the poem. Indeed Simone de Beauvoir documents the couple's reading habits in some detail in The Prime of Life, including their admiration for Hemingway and Faulkner during that time, but there is no mention of Eliot or Prufrock.2Both the poem and the novel present us with subjective, mood-laden impressions of the internal melancholic lives of their protagonists. Like Prufrock, Roquentin admits "My passion was dead."3Nausea is presented as a diary intended to be read by no one, and Prufrock is presented as a self-confession that no one is to hear. As Guido da Montefeltro in the poem's epigram is willing to speak to Dante because he believes Dante will never return to share what he has heard with the living, so Prufrock is solipsistically introspecting. The "you" of "Let us go then, you and I" is likely Prufrock addressing himself. But if it is addressed to another person, it can only be a reader who is as hopeless as he is, with no chance of return or redemption—only such a reader would really understand what is said. The final line of the poem "Till human voices wake us, and we drown" takes us back to the "patient etherized upon a table." Like Roquentin, Prufrock has taken himself and the reader [End Page 184] by proxy on an inner journey, a dream-like state in which the real and surreal come together.In the opening stanza of the poem, Prufrock describes his internal cityscape as including "Streets that follow like a tedious argument / Of insidious intent / To lead you to an overwhelming question... / Oh, do not ask, 'What is it?'" The question is mentioned twice more, but it is never articulated. Obviously it is an issue of great existential import concerning the meaning of life. Though Prufrock does not verbalize it, the question must be essentially Roquentin's question to himself: "Can you justify your existence then? Just a little?" (p. 177).As we shall see, even though Sartre's philosophy as developed in Nausea and crystallized in Being and Nothingness comes later and likely with no knowledge of Prufrock, the philosophy can still shed light on the poem—and in a way that in turn elucidates the philosophy.4IMeaning for Sartre is found in existence itself, emerging through the coloring and conceptualization of consciousness.5 While this does not necessarily imply the stereotypical existential view that life is bleak, meaningless, and possibly not worth living, this does nevertheless seem to be the conclusion that Roquentin draws early in Nausea. Consider this dark concern: "My existence began to worry me seriously. Was I not a simple spectre?" (p. 86). Early in the novel Roquentin concludes "Nothing happens while you live. The scenery changes, people come in and go out, that's all. There are no beginnings. Days are tacked on to days without rhyme or reason, an interminable, monotonous addition" (p. 39). This life as Roquentin describes it sounds eerily like the humdrum pointless existence of Prufrock, who has measured out his life with coffee spoons and spit out the butt-ends of his days and ways amidst the monotony of women who come and go talking of Michelangelo—a great man he resembles not at all.Later in the novel Roquentin admits "And it was true, I had always realized it; I hadn't the right to exist. I had appeared by chance, I existed like a stone, a plant or a microbe. My life put... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A "Hypostatic Union" of Two Practices but One Person?Paul F. KnitterThis is going to be an awkwardly personal reflection. But that, I understand, is what the assignment given to the members of the Society for Buddhist-Christian Studies panel "Constructing Buddhist Identities in the West" called for: I was asked to reflect upon "How I as a Western Christian have appropriated Buddhist practice and teachings into my religious identity." I'm (...) grateful for this invitation, because it has provided me with the occasion to realize, quite startlingly, that what I have thought and written about my "Buddhist-Christian identity" in the past really isn't quite accurate.But first let me offer a bird's eye, and therefore limited, view of my two-faced identity: I was born into a traditional, not very critical, Catholic family in the Chicago of seventy-three years ago. At thirteen, I decided (against my parents' wishes) to enter a minor seminary in order to become a priest, and went through the whole fourteen years of training. For the last four years of that training I had the profoundly good fortune to be sent to Rome, arriving there in 1962, two weeks before more than two thousand bishops marched into St. Peter's Basilica to start the Second Vatican Council (the renewing effects of which were much more lasting, it seems, in my psyche than in the psyche and structures of the Vatican!). Ordained a priest in 1966 and animated with Vatican II's new openness to other religions, I did a dissertation at the University of Marburg, Germany, on Christian theologies of religions. When I returned to the United States in 1972, I taught theology at Catholic Theological Union in Chicago, and when I decided to leave the Catholic priesthood in 1975, I moved to Xavier University in Cincinnati, where I continued teaching theology for some twenty-eight years.It was during those years, in the 1980s, that I began not only to teach courses on Buddhism but also to practice daily Zen meditation. Gradually, I came to realize that Buddhism, its theory and practice, was seeping into and coloring the way I understood and practiced my Christian creed—to the point that in 2007 I took refuge in the Tibetan Dzogchen tradition and since then have been under the guidance of my teacher, Lama John Makransky. It was around this time that I faced the need to figure out just what or who I was—a Buddhist Christian or a Christian Buddhist. So, typical academic that I am, I wrote a book. [End Page 19]In Without Buddha I Could Not Be a Christian, I declared and defended my primary identity as a Christian who was thoroughly drenched in Buddhism.1 But when I recently read Rose Drew's penetrating analysis of various ways of blending dual religious belonging in her Christian or Buddhist? An Exploration of Dual Religious Belonging, I started to wonder.2 From her ethnographic study of actual dual belongers, she found that (a) some have a primary religious identity (the group to which I thought I belonged), (b) some alternate between both primary identities, (c) some cannot attribute primacy to either or any identity, and (d) some are too bewildered by it all to say anything.3 As I pondered Drew's description and analysis of her interviewees' meanderings back and forth across religious lines, I had to admit that I wasn't sure where I belonged. So when the request for this paper came along, I saw it as an opportunity to help myself sort things out.An Inappropriate AnalogyMy problem is that as my Christian and Buddhist practices have continued over these recent five to ten years, more and more, I cannot keep them apart. They remain clearly distinct, but unlike Roger Corless, of blessed memory, I have not been able to honor their distinct identities by practicing them, as Roger apparently did, separately: being a Buddhist from Monday to Thursday, and a Christian from Friday to Sunday (and then waiting to see what would happen). Rather, for me, when I am at Mass, I hear the words of the Scripture readings or of... (shrink)

The idea that an utterance of a basic (nondeviant) declarative sentence expresses a single true-or-false proposition has dominated philosophical discussions of meaning in this century. Refinements aside, this idea is less of a substantive theses than it is a background assumption against which particular theories of meaning are evaluated. But there are phenomena (noted by Frege, Strawson, and Grice) that threaten at least the completeness of classical theories of meaning, which associate with an utterance of a simple sentence a truth-condition, (...) a Russellian proposition, or a Fregean thought. And it may well be the case that a framework within which utterances express sequences of propositions provides much of what is needed to account for the relevant phenomena, a better overall picture of the way language works, and an enticingly uniform perspective on a variety of semantic problems. I do not myself take to theories that multiply propositions by appealing to propositions “presupposed” or to pairs of Fregean and Russellian propositions, or theories that show no respect for a distinction between semantics and pragmatics— where the former is the study of propositions whose general form and character is determined by word meaning and syntax—or for theories that blithely abandon general principles of composition and semantic innocence. I would like to sketch a package based on four interconnected ideas: (i) the meaning of an individual word is a sequence of instructions for generating a sequence of propositions (in conjunction with compositional instructions (syntax) and elements of context); (ii) utterances themselves are not bearers of truth or falsity; (iii) judgements of truth, falsity, commitment, and conflict are shaped, in part, by the weights attached to individual 1 propositions that occur in sequences expressed by utterances, weights that may be set (and reset) by contextual considerations; (iv) Fregean senses are superfluous; propositions might as well be Russellian (Mont Blanc and all its snow fields will do as well as any mode of presentation).. (shrink)

Improving a theorem of Gasarch and Hirst, we prove that if 2 ≤ k ≤ m < ω, then the following is equivalent to WKL0 over RCA0 Every locally k-colorable graph is m-colorable.

It is consistent relative to an inaccessible cardinal that ZF+DC holds, and the hypergraph of isosceles triangles on $\mathbb {R}^2$ has countable chromatic number while the hypergraph of isosceles triangles on $\mathbb {R}^3$ has uncountable chromatic number.

Different explanations of color vision favor different philosophical positions: Computational vision is more compatible with objectivism (the color is in the object), psychophysics and neurophysiology with subjectivism (the color is in the head). Comparative research suggests that an explanation of color must be both experientialist (unlike objectivism) and ecological (unlike subjectivism). Computational vision's emphasis on optimally prespecified features of the environment (i.e., distal properties, independent of the sensory-motor capacities of the animal) is unsatisfactory. Conceiving of visual perception instead as the (...) visual guidance of activity in an environment that is determined largely by that very activity suggests new directions for research. (shrink)

One of Martin Heidegger’s enduring philosophical legacies is his overall vision of what it is to be us. We—whoever that turns out to include—are cases of Dasein, and as such we are distinctively open to entities, including others and ourselves. In this essay, I paint a picture of that openness that aims to capture why Heidegger’s vision has so powerfully gripped so many. Drawing on Heidegger’s thought both early and late, I present a synoptic view of us as (...) class='Hi'>open to the encounter with entities' bursting forth into presencing. We can be more or less closed off to this upsurge, but we can also allow it in its full power: in philosophical and poetic openness. I draw on Borgmann, Buber, Plato’s Socrates, Rilke, and others to capture our openness at its Heideggerian best—and we ourselves at our best, showing up radiantly for encounter. (shrink)

If [Formula: see text] is a closed Noetherian graph on a [Formula: see text]-compact Polish space with no infinite cliques, it is consistent with the choiceless set theory ZF[Formula: see text][Formula: see text][Formula: see text]DC that [Formula: see text] is countably chromatic and there is no Vitali set.

The age of global risks and changes that have come into play where stable development used to be a norm and the era of postmodernism, as a possibility of the multiplicity of meanings and solutions, determine the vectors of human development in the 21st century. Human society is undergoing changes, digital technologies are increasingly penetrating various domains of life, and it has become clear, they are here to stay because they are already changing life itself. The postmodern generation, consumed by (...) "virtual reality", sees the world differently. They need knowledge different from what previous generations used where knowledge itself requires new methods of education. With all positive and negative implications, the e-learning format has established itself as a viable education option in times of the world pandemic. The way this learning format transforms the higher education system is irrevocable. Thus, an increasing number of universities are integrating online and personalized components into their courses. However, the role of the teacher remains invariably important. Although methods and format of their work may adjust and alter, it is the teacher who passes on human experience, imbues knowledge with emotional coloring and encourages reflection and reasoning. Therefore, the e-learning system rests on two factors, namely, the presence on the Internet and the development of student-teacher relations. All available research and resources are currently aimed at improving technical capabilities, whereas the "student-learner" system needs to be reconsidered. It will not be destroyed in the new conditions, rather transformed into new forms. (shrink)

Nowadays, protecting trust in social sciences also means engaging in open community dialogue, which helps to safeguard robustness and improve efficiency of research methods. The combination of open data, open review and open dialogue may sound simple but implementation in the real world will not be straightforward. However, in view of Begley and Ellis’s (2012) statement that, “the scientific process demands the highest standards of quality, ethics and rigour,” they are worth implementing. More importantly, they are (...) feasible to work on and likely will help to restore plausibility to social sciences research. Therefore, I feel it likely that the triplet of open data, open review and open dialogue will gradually emerge to become policy requirements regardless of the research funding source. (shrink)

Textbook on Gödel’s incompleteness theorems and computability theory, based on the Open Logic Project. Covers recursive function theory, arithmetization of syntax, the first and second incompleteness theorem, models of arithmetic, second-order logic, and the lambda calculus.

A function is diagonally non-computable if it diagonalizes against the universal partial computable function. D.n.c. functions play a central role in algorithmic randomness and reverse mathematics. Flood and Towsner asked for which functions h, the principle stating the existence of an h-bounded d.n.c. function implies Ramsey-type weak König’s lemma. In this paper, we prove that for every computable order h, there exists an ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega}$$\end{document} -model of h-DNR which is not a not (...) model of the Ramsey-type graph coloring principle for two colors and therefore not a model of RWKL. The proof combines bushy tree forcing and a technique introduced by Lerman, Solomon and Towsner to transform a computable non-reducibility into a separation over ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\omega}$$\end{document} -models. (shrink)

We use methods of reverse mathematics to analyze the proof theoretic strength of a theorem involving the notion of coloring number. Classically, the coloring number of a graph $G=$ is the least cardinal $\kappa$ such that there is a well-ordering of $V$ for which below any vertex in $V$ there are fewer than $\kappa$ many vertices connected to it by $E$. We will study a theorem due to Komjáth and Milner, stating that if a graph is the union (...) of $n$ forests, then the coloring number of the graph is at most $2n$. We focus on the case when $n=1$. (shrink)

The end of human history is an event that has been foreseen or announced by both messianics and dialecticians. But who is the protagonist of that history that is coming—or has come—to a close? What is man? How did he come on the scene? And how has he maintained his privileged place as the master of, or first among, the animals? In The Open, contemporary Italian philosopher Giorgio Agamben considers the ways in which the “human” has been thought of (...) as either a distinct and superior type of animal, or a kind of being that is essentially different from animal altogether. In an argument that ranges from ancient Greek, Christian, and Jewish texts to twentieth-century thinkers such as Heidegger, Benjamin, and Kojève, Agamben examines the ways in which the distinction between man and animal has been manufactured by the logical presuppositions of Western thought, and he investigates the profound implications that the man/animal distinction has had for disciplines as seemingly disparate as philosophy, law, anthropology, medicine, and politics. (shrink)

Autism spectrum disorders reduce one’s ability to act appropriately in social situations. Increasing evidence indicates that children with ASD might ignore nonverbal social cues that usually aid social interaction because they do not recognize or understand them. We asked children with ASD to color an augmented reality coloring book to teach them how to recognize and understand some specific social signals and to ignore others. ARCB materials teach children to recognize and understand social signals in various ways. They can, (...) for example, view 3D animations of the ARCB materials on a tablet computer. Thus, the ARCB can be used to help children with ASD focus their attention on the meaning and social value of nonverbal behaviors in specific social situations. The ARCB has multiple functions: it extends the social features of the story, and it restricts attention to the most important parts of the videos. Single-subject research with a multiple-baselines across-subject design was used in this study. After five weeks of ARCB training intervention, all 3 participants’ scores rose significantly and dramatically during the intervention phase, and remained significantly higher in the maintenance phase than at baseline. We conclude that coloring pictures of social situations may help children with ASD recognize and better understand these situations. (shrink)

Why is education in the open society not open? Why is this option not even considered in the debate over which education is most suited for the open society? Many consider such an option irresponsible. What, then, are the minimal responsibilities of education? The present volume raises these questions and many more. It is a book we have been waiting for. It offers a rare combination of two seemingly opposite, unyielding attitudes: critical and friendly. Dr. Yehezkely applies (...) a rigorous fallibilist-critical approach to issues regarding contemporary education. His diagnosis is that the source of our trouble is the closed undemocratic character of education, which causes education to become, in effect, a fifth column in the open democratic society. Following Popper, he concedes that democracy is every bit as flawed and as problematic as its enemies accuse it of being, particularly in education; still it is our only hope, since open responsible debate of vital problems cannot do without it. Democracy is risky: yet its absence guarantees failure, especially in closed undemocratic education, even when inspired by the most progressive ideas extant, charged with tremendous good will, and executed with selfless love and devotion. Kibbutz education is a case in point. (shrink)

There is a deeply entrenched view in philosophy and physics, the closed systems view, according to which isolated systems are conceived of as fundamental. On this view, when a system is under the influence of its environment this is described in terms of a coupling between it and a separate system which taken together are isolated. We argue against this view, and in favor of the alternative open systems view, for which systems interacting with their environment are conceived of (...) as fundamental, and the environment's influence is represented via the dynamical equations that govern the system's evolution. Taking quantum theories of closed and open systems as our case study, and considering three alternative notions of fundamentality: (i) ontic fundamentality, (ii) epistemic fundamentality, and (iii) explanatory fundamentality, we argue that the open systems view is fundamental, and that this has important implications for the philosophy of physics, the philosophy of science, and for metaphysics. (shrink)

This paper defends traditional political philosophy against the challenges Gaus leverages against it in The Open Society and Its Complexities. Granting Gaus that consensus on the principles of political philosophy is not forthcoming and that complexity undermines many of our most ambitious reform efforts, the paper argues that much work remains for political philosophy as it has been practiced for centuries. This is for three reasons. First, Gaus's own defense of the open society requires resources from the very (...) traditions that he tends to dismiss. Secondly, the kinds of reform Gaus encourages us to focus on in light of complexity presuppose answers to philosophical questions, answers that philosophers have long attempted to provide. Thirdly, not all politically salient philosophical questions are aimed at action guidance. Despite the value in Gaus's analysis, I conclude that political philosophy's future will look, at least in part, like its storied past. (shrink)