DuBose, D.A., Determinacy and the sharp function on the reals, Annals of Pure and Applied Logic 55 237–263. We characterize in terms of determinacy, the existence of the least inner model of “every real has a sharp”. We let 1 be the sharp function on the reals and define two classes of sets, * and *+, which lie strictly between β<ω2 an d Δ. We show that the determinacy of * follows from L[#1] xvR; “every (...) class='Hi'>real has a sharp”; and we show that the existence of indiscernibles for L[#1] is equivalent to a slightly determinacy hypothesis, the determinacy of *+. (shrink)

For several partial sharp functions # on the reals, we characterize in terms of determinacy, the existence of indiscernibles for several inner models of “# exists for every real r”. Let #10=1#10 be the identity function on the reals. Inductively define the partial sharp function, β#1γ+1, on the reals so that #1γ+1 =1#1γ+1 codes indiscernibles for L [#11, #12,…, #1γ] and #1γ+1=#1γ+1). We sho w that the existence of β#1γ follows from the determinacy of *Σ01)*+ games . (...) Part I proves the converse. (shrink)

We characterize in terms of determinacy, the existence of the least inner model of “every real has a sharp”. We let #1 be the sharp function on the reals and define two classes of sets, * and *+, which lie strictly between β<ω2- and Δ. We show that the determinacy of * follows from L[#1] “every reak has a sharp”; and we show that the existence of indiscernibles for L[#1] is equivalent to a slightly stronger determinacy (...) hypothesis, the determinacy of *+. (shrink)

The theory of infinite games with slightly imperfect information has been developed for games with finitely and countably many moves. In this paper, we shift the discussion to games with uncountably many possible moves, introducing the axiom of real Blackwell determinacy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{Bl-AD}_\mathbb{R}}$$\end{document} (as an analogue of the axiom of real determinacy \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{AD}_\mathbb{R}}$$\end{document}). We prove that the consistency strength of (...) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathsf{Bl-AD}_\mathbb{R}}$$\end{document} is strictly greater than that of AD. (shrink)

Schmidt’s game and other similar intersection games have played an important role in recent years in applications to number theory, dynamics, and Diophantine approximation theory. These games are real games, that is, games in which the players make moves from a complete separable metric space. The determinacy of these games trivially follows from the axiom of determinacy for real games, $\mathsf {AD}_{\mathbb R}$, which is a much stronger axiom than that asserting all integer games are determined, (...) $\mathsf {AD}$. One of our main results is a general theorem which under the hypothesis $\mathsf {AD}$ implies the determinacy of intersection games which have a property allowing strategies to be simplified. In particular, we show that Schmidt’s $(\alpha,\beta,\rho )$ game on $\mathbb R$ is determined from $\mathsf {AD}$ alone, but on $\mathbb R^n$ for $n \geq 3$ we show that $\mathsf {AD}$ does not imply the determinacy of this game. We then give an application of simple strategies and prove that the winning player in Schmidt’s $(\alpha, \beta, \rho )$ game on $\mathbb {R}$ has a winning positional strategy, without appealing to the axiom of choice. We also prove several other results specifically related to the determinacy of Schmidt’s game. These results highlight the obstacles in obtaining the determinacy of Schmidt’s game from $\mathsf {AD}$. (shrink)

We give limits defined in terms of abstract pointclasses of the amount of determinacy available in certain canonical inner models involving strong cardinals. We show for example: Theorem A. $\mathrm{D}\mathrm{e}\mathrm{t}\text{\hspace{0.17em}}({\mathrm{\Pi }}_{1}^{1}-\mathrm{I}\mathrm{N}\mathrm{D})$ ⇒ there exists an inner model with a strong cardinal. Theorem B. Det(AQI) ⇒ there exist type-1 mice and hence inner models with proper classes of strong cardinals. where ${\mathrm{\Pi }}_{1}^{1}-\mathrm{I}\mathrm{N}\mathrm{D}\phantom{\rule{0ex}{0ex}}$ (AQI) is the pointclass of boldface ${\mathrm{\Pi }}_{1}^{1}$ -inductive (respectively arithmetically quasi-inductive) sets of reals.

From the hypothesis that all Turing closed games are determined we prove: (1) the Continuum Hypothesis and (2) every subset of ℵ1 is constructible from a real.

We prove that various classical tree forcings—for instance Sacks forcing, Mathias forcing, Laver forcing, Miller forcing and Silver forcing—preserve the statement that every real has a sharp and hence analytic determinacy. We then lift this result via methods of inner model theory to obtain level-by-level preservation of projective determinacy (PD). Assuming PD, we further prove that projective generic absoluteness holds and no new equivalence classes are added to thin projective transitive relations by these forcings.

We show under that every set of reals is I‐regular for any σ‐ideal I on the Baire space such that is proper. This answers the question of Khomskii [7, Question 2.6.5]. We also show that the same conclusion holds under if we additionally assume that the set of Borel codes for I‐positive sets is. If we do not assume, the notion of properness becomes obscure as pointed out by Asperó and Karagila [1]. Using the notion of strong properness similar to (...) the one introduced by Bagaria and Bosch [2], we show under without using that every set of reals is I‐regular for any σ‐ideal I on the Baire space such that is strongly proper assuming every set of reals is ∞‐Borel and there is no ω1‐sequence of distinct reals. In particular, the same conclusion holds in a Solovay model. (shrink)

We consider a seemingly weaker form of $\Delta ^{1}_{1}$ Turing determinacy.Let $2 \leqslant \rho < \omega _{1}^{\mathsf {CK}}$, $\textrm{Weak-Turing-Det}_{\rho }$ is the statement:Every $\Delta ^{1}_{1}$ set of reals cofinal in the Turing degrees contains two Turing distinct, $\Delta ^{0}_{\rho }$ -equivalent reals.We show in $\mathsf {ZF}^-$ : $\textrm{Weak-Turing-Det}_{\rho }$ implies: for every $\nu < \omega _{1}^{\mathsf {CK}}$ there is a transitive model ${M \models \mathsf {ZF}^{-} + \textrm{``}\aleph _{\nu } \textrm{ exists''.}}$ As a corollary:If every cofinal $\Delta ^{1}_{1}$ set (...) of Turing degrees contains both a degree and its jump, then for every $\nu < \omega_1^{\mathsf{CK}}$, there is atransitive model: $M \models \mathsf{ZF}^{-} + \textrm{``}\aleph_\nu \textrm{ exists''.}$ •With a simple proof, this improves upon a well-known result of Harvey Friedman on the strength of Borel determinacy.•Invoking Tony Martin’s proof of Borel determinacy, $\textrm{Weak-Turing-Det}_{\rho }$ implies $\Delta ^{1}_{1}$ determinacy.•We show further that, assuming $\Delta ^{1}_{1}$ Turing determinacy, or Borel Turing determinacy, as needed:–Every cofinal $\Sigma ^{1}_{1}$ set of Turing degrees contains a “hyp-Turing cone”: ${\{x \in \mathcal {D} \mid d_{0} \leqslant _{T} x \leqslant _{h} d_{0} \}}$.–For a sequence $_{k < \omega }$ of analytic sets of Turing degrees, cofinal in $\mathcal {D}$, $\bigcap _{k} A_{k}$ is cofinal in $\mathcal {D}$. (shrink)

Let Mn♯ denote the minimal active iterable extender model which has n Woodin cardinals and contains all reals, if it exists, in which case we denote by Mn the class-sized model obtained by iterating the topmost measure of Mn class-many times. We characterize the sets of reals which are Σ1-definable from R over Mn, under the assumption that projective games on reals are determined:1. for even n, Σ1Mn=⅁RΠn+11;2. for odd n, Σ1Mn=⅁RΣn+11.This generalizes a theorem of Martin and Steel for L, (...) that is, the case n=0. As consequences of the proof, we see that determinacy of all projective games with moves in R is equivalent to the statement that Mn♯ exists for all n∈N, and that determinacy of all projective games of length ω2 with moves in N is equivalent to the statement that Mn♯ exists and satisfies AD for all n∈N. (shrink)

We prove within K\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${K}$$\end{document} that the axiom of determinacy is equivalent to the assertion that for each ordinal λ λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa > \lambda}$$\end{document}. Here Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\Theta}$$\end{document} is the supremum of the ordinals which are the surjective image of the set of reals R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document}.

We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. (...) A consequence is the Determinacy Transfer Theorem for arbitrary [Formula: see text], namely the statement that [Formula: see text] determinacy implies [Formula: see text] determinacy. (shrink)

We prove the following result which is due to the third author. Let [Formula: see text]. If [Formula: see text] determinacy and [Formula: see text] determinacy both hold true and there is no [Formula: see text]-definable [Formula: see text]-sequence of pairwise distinct reals, then [Formula: see text] exists and is [Formula: see text]-iterable. The proof yields that [Formula: see text] determinacy implies that [Formula: see text] exists and is [Formula: see text]-iterable for all reals [Formula: see text]. (...) A consequence is the Determinacy Transfer Theorem for arbitrary [Formula: see text], namely the statement that [Formula: see text] determinacy implies [Formula: see text] determinacy. (shrink)

We show that the Axiom of Dependent Choice,, holds in countably iterable, passive premice constructed over their reals which satisfy the Axiom of Determinacy,, in a background universe. This generalizes an argument of Kechris for using Steel's analysis of scales in mice. In particular, we show that for any and any countable set of reals A so that and, we have that.

We determine the consistency strength of determinacy for projective games of length ω^2. Our main theorem is that $\Pi _{n + 1}^1$-determinacy for games of length ω^2 implies the existence of a model of set theory with ω + n Woodin cardinals. In a first step, we show that this hypothesis implies that there is a countable set of reals A such that M_n(A), the canonical inner model for n Woodin cardinals constructed over A, satisfies $A = R$ (...) and the Axiom of Determinacy. Then we argue how to obtain a model with ω + n Woodin cardinal from this. We also show how the proof can be adapted to investigate the consistency strength of determinacy for games of length ω^2 with payoff in $R^R\Pi _1^1$ or with σ-projective payoff. (shrink)

It is shown that the determinacy of $G_{\delta \sigma }$ games of length $\omega ^2$ is equivalent to the existence of a transitive model of ${\mathsf {KP}} + {\mathsf {AD}} + \Pi _1\textrm {-MI}_{\mathbb {R}}$ containing $\mathbb {R}$. Here, $\Pi _1\textrm {-MI}_{\mathbb {R}}$ is the axiom asserting that every monotone $\Pi _1$ operator on the real numbers has an inductive fixpoint.

We show that if Ƒ is any "well-behaved" subset of the Borei functions and we assume the Axiom of Determinacy then the hierarchy of degrees on $P(^\omega \omega )$ induced by Ƒ turns out to look like the Wadge hierarchy (which is the special case where Ƒ is the set of continuous functions).

We show that assuming the determinacy of all games on reals, every set of reals is \ universally baire.

We investigate Turing cones as sets of reals, and look at the relationship between Turing cones, measures, Baire category and special sets of reals, using these methods to show that Martin's proof of Turing Determinacy (every determined Turing closed set contains a Turing cone or is disjoint from one) does not work when you replace “determined” with “Blackwell determined”. This answers a question of Tony Martin.

We show that assuming the determinacy of all games on reals, every set of reals is Θ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta $$\end{document} universally baire.

Aristoteles (384-322 a.C.), es uno de los pensadores mas influyentes de la historia de la humanidad. Filosofo y cientifico, su obra incorpora una gran variedad de conocimientos que, a traves de la pedagogia directa, transmitio a sus alumnos. Metafisica es una obra magna del pensamiento occidental, compuesta de catorce libros -de los que presentamos una seleccion- representa un compendio de todo el saber aristotelico en el campo de la filosofia y, tambien, un elemento basico de la misma como ciencia del (...) saber y del conocimiento. Todos los problemas que ha debatido la metafisica hasta hoy tienen su origen en las ideas que Aristoteles plantea y desarrolla en este libro de libros. (shrink)

Neste livro, o autor relaciona aspectos filosóficos, sociológicos e jurídicos, abordando temas essenciais à introdução ao estudo do Direito, como a estrutura, validade e classificação da norma jurídica, as fontes e os princípios gerais do Direito e a hermenêutica jurídica. Encontra-se totalmente adaptado à Lei n. 10.406/2002, que instituiu o novo Código Civil.

Esta obra traz o estudo correlato da política e do direito, fundamental para a compreensão dessas duas ciências e da democracia. Aqui encontramos proposições como Estado e soberania, Estado e direito e a análise do poder do Estado nos domínios do saber político. Em suma, esta clássica obra representa valiosa contribuição para o pensamento jurídico e político, tornando-se indispensável apar os cultores da ciência jurídica.

Reale's monumental work establishes the exact dimensions of Aristotle's concept of first philosophy and proves the profound unity of concept that exists in Aristotle's Metaphysics.

This study investigates the engagement of family firms in corporate social responsibility. We first compare their corporate social performance to non-family firms. Then, following recent evidence on the heterogeneity of family firms, we examine two factors that may influence CSP within family firms: the level of family control and the governance orientation of the country in which they operate. This research is based on a theoretical framework which considers both agency and socioemotional wealth influences on family firms CSR engagements. Overall, (...) we find that family firms exhibit lower CSP than non-family firms. But when focusing on family firms, our analyses show a curvilinear relationship between family control and CSP. At lower levels of control, family owners invest more in social initiatives to protect their SEW. Beyond a threshold level of control that we estimate at 36 % in our sample, economic considerations prevail over SEW and social performance starts decreasing. We also find that family firms operating in stakeholder-oriented countries are more attentive to social concerns than those operating in more shareholder-oriented countries. (shrink)

Foucault’s work is rich enough to sustain multiple readings. I argue in this paper for the continued construction and maintenance of what I have called the ‘American Foucault’, whose principal preoccupation is with the question of how to be free within our contemporary political constraints and possibilities. (Such a Foucault can be found in the works of American writers such as W. E. Connolly, Todd May, and Thomas Dumm.) Appreciation of Foucault’s contribution to an understanding of freedom is too often (...) hampered, however, by the insistence on the part of many of the most influential of Foucault’s critics (and some of his defenders) that his particular mode of thinking is ultimately too irresponsible. It is thought that Foucault’s refusal to account for the grounds of his work vitiates his overall project. I argue that, if we distinguish between the ‘account-ability’ demanded by his critics and the ‘response-ability’ that his work permits, we will be in a better position to appreciate the timeliness of his conception of freedom. (shrink)

This article proposes and empirically tests a theoretical framework incorporating Reidenbach and Robin’s (J Bus Ethics 10(4):273–284, 1991 ) conceptual model of corporate moral development. The framework is used to examine the relation between governance and business ethics, as proxied by diversity management (DM), and financial reporting quality, as proxied by the magnitude of earnings management (EM). The level of DM and governance quality are measured in accordance with the ratings of Jantzi Research (JR), a leading provider of social and (...) governance research for institutional investors. This DM score is part of an index developed by JR that investment managers use to integrate DM criteria into their investment decisions. As expected, a negative relation between corporate DM development and financial reporting quality is found while controlling for other factors known in the literatures on governance and accounting choices to affect earnings quality. Despite some caveats presented in conclusion, this study contributes to the ethics, governance, and financial reporting literatures by studying the dynamics between governance and ethics in the prevention of EM. (shrink)

-- v. 5. V. słownik, indeksy i bibliografia.

While COVID-19 has generated a massive burden of illness worldwide, healthcare workers (HCWs) have been disproportionately exposed to SARS-CoV-2 coronavirus infection. During the so-called ‘first wave’, infection rates among this population group have ranged between 10% and 20%, raising as high as one in every four COVID-19 patients in Spain at the peak of the crisis. Now that many countries are already dealing with new waves of COVID-19 cases, a potential competition between HCW and non-HCW patients for scarce resources can (...) still be a likely clinical scenario. In this paper, we address the question of whether HCW who become ill with COVID-19 should be prioritised in diagnostic, treatment or resource allocation protocols. We will evaluate some of the proposed arguments both in favour and against the prioritisation of HCW and also consider which clinical circumstances might warrant prioritising HCW and why could it be ethically appropriate to do so. We conclude that prioritising HCW’s access to protective equipment, diagnostic tests or even prophylactic or therapeutic drug regimes and vaccines might be ethically defensible. However, prioritising HCWs to receive intensive care unit (ICU) beds or ventilators is a much more nuanced decision, in which arguments such as instrumental value or reciprocity might not be enough, and economic and systemic values will need to be considered. (shrink)

Although shared decision-making is a standard in medical care, unilateral decisions through process-based conflict resolution policies have been defended in certain cases. In patients who do not stand to receive proportional clinical benefits, the harms involved in interventions such as cardiopulmonary resuscitation seem to run contrary to the principle of non-maleficence, and provision of such interventions may cause clinicians significant moral distress. However, because the application of these policies involves taking choices out of the domain of shared decision-making, they face (...) important ethical and legal problems, including a recent challenge to their constitutionality. In light of these concerns, we suggest a re-conceptualization of informed non-dissent as an alternative approach in cases where the application of process-based policies is being considered. This clinician-directed communication model still preserves what is valuable in such policies and salvages professional integrity, while minimising ethical and legal challenges. (shrink)