We introduce a new method for building models of [Formula: see text], together with [Formula: see text] statements over [Formula: see text], by forcing. Unlike other forcing constructions in the literature, our construction adds new reals, although only [Formula: see text]-many of them. Using this approach, we build a model in which a very strong form of the negation of Club Guessing at [Formula: see text] known as [Formula: see text] holds together with [Formula: see text], thereby answering a well-known (...) question of Moore. This construction can be described as a finite-support weak forcing iteration with side conditions consisting of suitable graphs of sets of models with markers. The [Formula: see text]-preservation is accomplished through the imposition of copying constraints on the information carried by the condition, as dictated by the edges in the graph. (shrink)

In this paper we build an Asperó–Mota iteration of length $\omega _2$ that adds a family of $\aleph _2$ many club subsets of $\omega _1$ which cannot be diagonalized while preserving $\aleph _2$. This result discloses a technical limitation of some types of Asperó–Mota iterations.

It is possible to control to a large extent, via semiproper forcing, the parameters measuring the guessing density of the members of any given antichain of stationary subsets of ω1 . Here, given a pair of ordinals, we will say that a stationary set Sω1 has guessing density if β0=γ and , where γ is, for every stationary S*ω1, the infimum of the set of ordinals τ≤ω1+1 for which there is a function with ot)<τ for all νS* and with {νS*:gF} (...) stationary for every α<ω2 and every canonical function g for α. This work involves an analysis of iterations of models of set theory relative to sequences of measures on possibly distinct measurable cardinals. As an application of these techniques I show how to force, from the existence of a supercompact cardinal, a model of in which there is a well-order of H definable, over H,, by a formula without parameters. (shrink)

The Theme. Strong forcing axioms like Martin’s Maximum give a reasonably satisfactory structural analysis of $H(\omega _2)$. A broad program in modern Set Theory is searching for strong forcing axioms beyond $\omega _1$. In other words, one would like to figure out the structural properties of taller initial segments of the universe. However, the classical techniques of forcing iterations seem unable to bypass the obstacles, as the resulting forcings axioms beyond $\omega _1$ have not thus far been strong enough! However, (...) with his celebrated work on generalised side conditions, I. Neeman introduced us to a novel paradigm to iterate forcings. In particular, he could, among other things, reprove the consistency of the Proper Forcing Axiom using an iterated forcing with finite supports. In 2015, using his technology of virtual models, Veličković built up an iteration of semi-proper forcings with finite supports, hence reproving the consistency of Martin’s Maximum, an achievement leading to the notion of a virtual model.In this thesis, we are interested in constructing forcing notions with finitely many virtual models as side conditions to preserve three uncountable cardinals. The thesis constitutes six chapters and three appendices that amount to 118 pages, where Section 1 is devoted to preliminaries, and Section 2 is a warm-up about the scaffolding poset of a proper forcing. In Section 3, we present the general theory of virtual models in the context of forcing with sets of models of two types, where we, e.g., define the “meet” between two virtual models and prove its properties.The main results are joint with Boban Veličković, and partly appeared in Guessing models and the approachability ideal, J. Math. Log. 21 (2021).Pure Side Conditions. In Section 4, we use two types of virtual models (countable and large non-transitive ones induced by a supercompact cardinal, which we call Magidor models) to construct our forcing with pure side conditions. The forcing covertly uses a third type of models that are transitive. We also add decorations to the conditions to add many clubs in the generic $\omega _2$. In contrast to Neeman’s method, we do not have a single chain, but $\alpha $ -chains, for an ordinal $\alpha $ with $V_\alpha \prec V_\lambda $. Thus, starting from suitable large cardinals $\kappa <\lambda $, we construct a forcing notion whose conditions are finite sets of virtual models described earlier. The forcing is strongly proper, preserves $\kappa $, and has the $\lambda $ -Knaster property. The relevant quotients of the forcing are strongly proper, which helps us prove strong guessing model principles. The construction is generalisable to a ${<}\mu $ -closed forcing, for any given cardinal $\mu $ with $\mu ^{<\mu }=\mu <\kappa $.The Iteration Theorem. In Section 5, we use the forcing with pure side conditions to iterate a subclass of proper and $\aleph _2$ -c.c. forcings and obtain a forcing axiom at the level of $\aleph _2$. The iterable class is closely related to Asperó–Mota’s forcing axiom for finitely proper forcings.Guessing Model Principles. Section 6 encompasses the main parts of the thesis. We prove the consistency of the guessing principle $\mathrm {GMP}^+(\omega _3,\omega _1)$ that states for any cardinal ${\theta \geq \omega _3}$, the set of $\aleph _2$ -sized elementary submodels M of $H(\theta )$, which are the union of an $\omega _1$ -continuous $\in $ -chain of $\omega _1$ -guessing, I.C. models is stationary in $\mathcal P_{\omega _3}(H(\theta ))$. The consistency and consequences of this principle are demonstrated in the following diagram. We also prove that one can obtain the above guessing models in a way that the $\omega _1$ -sized $\omega _1$ -guessing models remain $\omega _1$ -guessing model in any outer transitive model with the same $\omega _1$, and we denote this principle by $\rm{SGMP}^+(\omega_3,\omega_1)$.In the following diagram, $\mathrm{TP}$ stands for the tree property; $w\mathrm{KH}$ stands for the weak Kurepa Hypothesis; $\mathrm{MP}$ stands for Mitchell property, i.e., the approachability ideal is trivial modulo the nonstationary ideal; $\mathrm{AP}$ stands for the approachability property; $\mathrm {AMTP}(\kappa ^+)$ states that if $2^\kappa <\aleph _{\kappa ^+}$, then every forcing which adds a new subset of $\kappa ^+$ whose initial segments are in the ground model, collapses some cardinal $\leq 2^{\kappa }$. The dotted arrow denotes the relative consistency, while others are logical implications.Appendices. Appendix A includes merely the above diagram. Appendix B presents a proof of the Mapping Reflection Principle with finite conditions under $\mathrm {PFA}$. Appendix C contains open problems. Finally, the thesis’s bibliography consists of 42 items.Abstract prepared by Rahman MohammadpourE-mail: [email protected]: https://theses.hal.science/tel-03209264. (shrink)

O objetivo deste artigo é, primeiro, apresentar e considerar as críticas de Paley com mais detalhes e, em seguida, discutir algumas das aplicações significativas da fenomenologia que muitas vezes foram negligenciadas pelos pesquisadores qualitativos. Como foi amplamente demonstrado ao longo dos anos, a fenomenologia pode não apenas fazer a diferença no manuseio, análise e interpretação dos dados disponíveis, mas também em como os dados são obtidos em primeiro lugar, por exemplo, através de técnicas especiais de entrevista. Consideraremos algumas figuras centrais (...) da psicologia fenomenológica clássica e da psiquiatria fenomenológica e apresentaremos alguns dos desenvolvimentos mais recentes na ciência cognitiva. Em seguida, discutiremos três casos concretos que demonstram como a fenomenologia foi aplicada no trabalho clínico com pacientes com esquizofrenia, paralisia cerebral e negligência hemispatial. (shrink)

Accountability is a quality often demanded of the church and its leaders today, and especially so within the Roman Catholic Church. But how should accountability itself be understood, and how might a more accountable church be achieved? This essay explores these questions from a new angle by offering a detailed ethical analysis of how accountability operates within broad-based community organizing (BBCO), a form of democratic politics with a highly developed theory and practice of accountability in which many churches already participate. (...) In dialogue with BBCO, the essay develops a constructive framework for conceptualizing accountability. It makes a case for understanding accountability principally as a property of reciprocal relationships between persons, and stresses the need to proactively cultivate and sustain relationships of accountability through ongoing democratic practices of accountability. It also highlights the role played by moral authority, power, and virtue in these relationships and practices. The essay concludes by using this framework to propose a new interpretation of the Catholic Church’s accountability crisis. It suggests a more accountable church may only be achieved when the whole people of God begin organizing themselves to build it. (shrink)

We prove that a form of the $Erd\H{o}s$ property (consistent with $V = L\lbrack H_{\omega_2}\rbrack$ and strictly weaker than the Weak Chang's Conjecture at ω1), together with Bounded Martin's Maximum implies that Woodin's principle $\psi_{AC}$ holds, and therefore 2ℵ0 = ℵ2. We also prove that $\psi_{AC}$ implies that every function $f: \omega_1 \rightarrow \omega_1$ is bounded by some canonical function on a club and use this to produce a model of the Bounded Semiproper Forcing Axiom in which Bounded Martin's Maximum (...) fails. (shrink)

Etnofiction essay, between anthropology and philosophy.

Summary In the period between the two World Wars, the Portuguese Geological Survey (Serviços Geológicos de Portugal: PGS) was legally dependent on the General Directorate of Mines and Geological Survey (Direcção Geral de Minas e Serviços Geológicos: GDMGS). Portugal was then living through troubled times, and the PGS struggled with financial problems and a lack of technical personnel. This situation did not allow the PGS to work properly as a scientific institution, and achieve its main function: the making and publication (...) of geological maps and research papers. (shrink)

Este trabalho tem por objetivo apresentar algumas considerações sobre a noção da experiência no âmbito da filosofia da educação. Na transposição dos ideais formativos iluminista e romântico para os sistemas escolares ocorre a marginalização da experiência, a centralidade das noções modelares hegemônicas (a cientifica-especializada e a crítica-reflexiva) e o problema da redução da experiência ao empírico. Na contemporaneidade, indicamos caminhos alternativos para a retomada da experiência no campo de estudos da filosofia da educação.

to be or not to be ethically neutral, in a world of decieve and calculation.

By forcing over a model of with a class-sized partial order preserving this theory we produce a model in which there is a locally defined well-order of the universe; that is, one whose restriction to all levels H is a well-order of H definable over the structure H, by a parameter-free formula. Further, this forcing construction preserves all supercompact cardinals as well as all instances of regular local supercompactness. It is also possible to define variants of this construction which, in (...) addition to forcing a locally defined well-order of the universe, preserve many of the n-huge cardinals from the ground model. (shrink)

We develop a general framework for forcing with coherent adequate sets on [Formula: see text] as side conditions, where [Formula: see text] is a cardinal of uncountable cofinality. We describe a class of forcing posets which we call coherent adequate type forcings. The main theorem of the paper is that any coherent adequate type forcing preserves CH. We show that there exists a forcing poset for adding a club subset of [Formula: see text] with finite conditions while preserving CH, solving (...) a problem of Friedman [Forcing with finite conditions, in Set Theory: Centre de Recerca Matemática, Barcelona, 2003–2004, Trends in Mathematics, pp. 285–295.]. (shrink)

Journal of Mathematical Logic, Volume 22, Issue 02, August 2022. We introduce bounded category forcing axioms for well-behaved classes [math]. These are strong forms of bounded forcing axioms which completely decide the theory of some initial segment of the universe [math] modulo forcing in [math], for some cardinal [math] naturally associated to [math]. These axioms naturally extend projective absoluteness for arbitrary set-forcing — in this situation [math] — to classes [math] with [math]. Unlike projective absoluteness, these higher bounded category forcing (...) axioms do not follow from large cardinal axioms but can be forced under mild large cardinal assumptions on [math]. We also show the existence of many classes [math] with [math] giving rise to pairwise incompatible theories for [math]. (shrink)

We show that Dependent Choice is a sufficient choice principle for developing the basic theory of proper forcing, and for deriving generic absoluteness for the Chang model in the presence of large cardinals, even with respect to $\mathsf {DC}$ -preserving symmetric submodels of forcing extensions. Hence, $\mathsf {ZF}+\mathsf {DC}$ not only provides the right framework for developing classical analysis, but is also the right base theory over which to safeguard truth in analysis from the independence phenomenon in the presence of (...) large cardinals. We also investigate some basic consequences of the Proper Forcing Axiom in $\mathsf {ZF}$, and formulate a natural question about the generic absoluteness of the Proper Forcing Axiom in $\mathsf {ZF}+\mathsf {DC}$ and $\mathsf {ZFC}$. Our results confirm $\mathsf {ZF} + \mathsf {DC}$ as a natural foundation for a significant portion of “classical mathematics” and provide support to the idea of this theory being also a natural foundation for a large part of set theory. (shrink)

Assuming ${2^{{N_0}}}$ = N₁ and ${2^{{N_1}}}$ = N₂, we build a partial order that forces the existence of a well-order of H(ω₂) lightface definable over ⟨H(ω₂), Є⟩ and that preserves cardinal exponentiation and cofinalities.

Este artículo discute el problema de la permanencia y del cambio. Empieza considerando al esencialismo frente al anti-esencialismo contemporáneo, en un segundo momento, la noción de existencia y, en seguida, las de identidad y cambio. Finalmente, se apela a la naturaleza de la predicación para mostrar que, contra el esencialista, la concepción del cambio de su contrincante sí logra resolver el problema de la unidad semántica de la proposición.

I define a homogeneous \–c.c. proper product forcing for adding many clubs of \ with finite conditions. I use this forcing to build models of \=\aleph _2\), together with \\) and \ large and with very strong failures of club guessing at \.

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)

After presenting a general setting in which to look at forcing axioms, we give a hierarchy of generalized bounded forcing axioms that correspond level by level, in consistency strength, with the members of a natural hierarchy of large cardinals below a Mahlo. We give a general construction of models of generalized bounded forcing axioms. Then we consider the bounded forcing axiom for a class of partially ordered sets Γ 1 such that, letting Γ 0 be the class of all stationary-set-preserving (...) partially ordered sets, one can prove the following: (a) $\Gamma_0 \subseteq \Gamma_1$ , (b) Γ 0 = Γ 1 if and only if NS ω 1 is ℵ 1 -dense. (c) If P $\notin \Gamma_1$ , then BFA({P}) fails. We call the bounded forcing axiom for Γ 1 Maximal Bounded Forcing Axiom (MBFA). Finally we prove MBFA consistent relative to the consistency of an inaccessible Σ 2 -correct cardinal which is a limit of strongly compact cardinals. (shrink)

There is a partial order ${\mathbb{P}}$ preserving stationary subsets of ω 1 and forcing that every partial order in the ground model V that collapses a sufficiently large ordinal to ω 1 over V also collapses ω 1 over ${V^{\mathbb{P}}}$ . The proof of this uses a coding of reals into ordinals by proper forcing discovered by Justin Moore and a symmetric extension of the universe in which the Axiom of Choice fails. Also, using one feature of the proof of (...) the above result together with an argument involving the stationary tower it is shown that sometimes, after adding one Cohen real c, there are, for every real a in V[c], sets A and B such that c is Cohen generic over both L[A] and L[B] but a is constructible from A together with B. (shrink)

Given any subset A of ω1 there is a proper partial order which forces that the predicate xA and the predicate xω1A can be expressed by -provably incompatible Σ3 formulas over the structure Hω2,,NSω1. Also, if there is an inaccessible cardinal, then there is a proper partial order which forces the existence of a well-order of Hω2 definable over Hω2,,NSω1 by a provably antisymmetric Σ3 formula with two free variables. The proofs of these results involve a technique for manipulating the (...) guessing properties of club-sequences defined on stationary subsets of ω1 at will in such a way that the Σ3 theory of Hω2,,NSω1 with countable ordinals as parameters is forced to code a prescribed subset of ω1. On the other hand, using theorems due to Woodin it can be shown that, in the presence of sufficiently strong large cardinals, the above results are close to optimal from the point of view of the Levy hierarchy. (shrink)

In this research, we evaluate the response of Brazilian consumers to corporate social responsibility (CSR) initiatives accompanied by a price increase. We demonstrate that the extent to which Brazilian consumers perceive a company to be socially responsible (i.e., their CSR perceptions) is related to both the basic transactional outcome of purchase intentions as well as two relational outcomes: the likelihood to switch to a competitor and to complain about the CSR-based price increase. More interestingly, we find that these relationships are (...) jointly mediated by the consumers’ perceptions of price fairness and feelings of personal satisfaction. Perhaps most interesting, we find that these mediating effects vary with consumer purchasing power; the mediating effect of price fairness on purchase intention is stronger for lower income than for higher income consumers, whereas the mediating effects of personal satisfaction on switching and complaining intentions are stronger for higher income than for lower income consumers. (shrink)

A violência contra a mulher é uma realidade mundial estabelecida nas desigualdades de gênero e perpetuada por discursos culturais e sociais. O acesso e uso de informações precisas e atualizadas sobre diferentes formas de violência são fundamentais para romper o ciclo de agressão e da falta de conhecimento sobre direitos e leis de proteção. Nesta perspectiva, é mister entender o comportamento informacional e fomentar a Competência Informacional das mulheres vítimas da violência de gênero. O presente artigo se propõe a tecer (...) considerações sobre as deficiências sociais, políticas e operacionais existentes na esfera de amparo e proteção às mulheres vítimas de violência (s). Como resultado, propõe a construção de um modelo de rede pautado na intersecção mulher-informação-órgãos de apoio e proteção contra à(s) violência(s), fundamentada nas competências em informação de modo concomitante. (shrink)

No período pandêmico ocasionado pelo Novo Coronavírus, surgiram muitas Fake News nas redes sociais digitais, gerando desinformação e prejudicando a Administração Pública na contenção de novos casos. Demonstra-se por meio da análise da publicização dos boletins epidemiológicos da Covid-19, disseminados nas redes sociais do Governo do Estado de Alagoas, a importância da transparência nas informações de interesse público. Essas redes, principais meios de comunicação e informação da sociedade, têm alto poder de disseminação informacional, cujo potencial “viral”, proporcionado pela instantaneidade e (...) interatividade, alcança uma infinidade de públicos. Como espaços férteis para o surgimento de Fake News e desinformação, podem gerar crises de confiabilidade e veracidade quanto às informações divulgadas pelo Governo, bem como não estimular o alagoano ao exercício da cidadania, nem agregar valor a essa sociedade. A partir do exposto, constata-se que a informação, nesse ambiente digital, deve ser tratada de forma crível, clara e responsável, com vistas a gerar maior confiabilidade, interação e acesso à informação de interesse social, bem como contribuir para a redução da circulação de Fake News e Desinformação. Adotou-se as pesquisas documental e qualitativa com uma abordagem exploratória, realizando-se a coleta de dados nas redes sociais oficiais do governo alagoano: Facebook, Instagram e Twitter. (shrink)

We isolate natural strengthenings of Bounded Martin’s Maximum which we call ${\mathsf{BMM}}^{*}$ and $A-{\mathsf{BMM}}^{*,++}$, and we investigate their consequences. We also show that if $A-{\mathsf{BMM}}^{*,++}$ holds true for every set of reals $A$ in $L$, then Woodin’s axiom $$ holds true. We conjecture that ${\mathsf{MM}}^{++}$ implies $A-{\mathsf{BMM}}^{*,++}$ for every $A$ which is universally Baire.

Several situations are presented in which there is an ordinal γ such that ${\{ X \in [\gamma]^{\aleph_0} : X \cap \omega_1 \in S\,{\rm and}\, ot(X) \in T \}}$ is a stationary subset of ${[\gamma]^{\aleph_0}}$ for all stationary ${S, T\subseteq \omega_1}$ . A natural strengthening of the existence of an ordinal γ for which the above conclusion holds lies, in terms of consistency strength, between the existence of the sharp of ${H_{\omega_2}}$ and the existence of sharps for all reals. Also, an (...) optimal model separating Bounded Semiproper Forcing Axiom (BSPFA) and Bounded Martin’s Maximum (BMM) is produced and it is shown that a strong form of BMM involving only parameters from ${H_{\omega_2}}$ implies that every function from ω 1 into ω 1 is bounded on a club by a canonical function. (shrink)

Working under large cardinal assumptions such as supercompactness, we study the Borel reducibility between equivalence relations modulo restrictions of the nonstationary ideal on some fixed cardinal κ. We show the consistency of Eλ-clubλ++,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλλ++ in the space λ++, being continuously reducible to Eλ+-club2,λ++, the relation of equivalence modulo the nonstationary ideal restricted to Sλ+λ++ in the space 2λ++. Then we show that for κ ineffable Ereg2,κ, the relation of equivalence modulo (...) the nonstationary ideal restricted to regular cardinals in the space 2κ is Σ11-complete. We finish by showing that, for Π21-indescribable κ, the isomorphism relation between dense linear orders of cardinality κ is Σ11-complete. (shrink)

Public pressure is essential for providing multinational enterprises (MNEs) with motivation to follow the standards of human rights conduct set in soft-law instruments, such as the United Nations Guiding Principles on Business and Human Rights. But how does the public judge MNE involvement in human rights violations? We empirically answer this question drawing on an original survey of American adults. We asked respondents to judge over 12,000 randomly generated scenarios in which MNEs may be considered to have been involved in (...) human rights violations. Our findings reveal substantial gaps between public judgments and the standards set in soft law and the normative literature. We identify the attributes of episodes of human rights violations involving MNEs that influence public judgments, including the relationship between the MNE and the perpetrator, the practice of due diligence, and the type of abuse. These results provide insights as to when we might expect public pressure to drive MNE compliance with soft-law instruments, and they direct attention to specific standards that will likely require stronger, ‘hard’ law approaches or broader efforts to shift the public’s view. (shrink)

The organization of the Herodotian narrative is based overall in the characterization of the despotism, however this can only mean something in Herodotus‟ work if opposed to the Greek ways of political organization and mainly in relation to democracy. However, the fact that the barbarians‟ despotism takes higher evidence in the work is enough to make the theme of tyranny dominate over the poliada organization? Could not we assume that the distinction of tyranny would not be only one way to (...) show the Greeks their own particularity? In this case, the exotic one, marvelous and the admirable one would lie in the fact that the Greeks organized a completely singular way of political organization, stranger to all the other known peoples. (shrink)