Our main results are: (A) It is consistent relative to a large cardinal that holds but fails. (B) If holds and are two infinite cardinals such that and λ carries a good scale, then holds. (C) If are two cardinals such that κ is λ‐Shelah and, then there is no good scale for λ.

Let μ,κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu, \kappa}$$\end{document} and λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\lambda}$$\end{document} be three uncountable cardinals such that μ=cf<κ=cf<λ.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu = {\rm cf} < \kappa = {\rm cf} < \lambda.}$$\end{document} The game ideal NGκ,λμ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${NG_{\kappa,\lambda}^\mu}$$\end{document} is a normal ideal on Pκ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${P_\kappa }$$\end{document} defined using games (...) of length μ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu}$$\end{document}. We show that if 2≤λ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${2^{} \leq \lambda}$$\end{document} and there are no large cardinals in an inner model, then the diamond principle ♢κ,λ[NGκ,λμ]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamondsuit_{\kappa,\lambda} [{NG}_{\kappa,\lambda}^\mu]}$$\end{document} holds. We also show that if ♢κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamondsuit_\kappa }$$\end{document} holds, where S is a stationary subset of κ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\kappa}$$\end{document}, then ♢κ,λ:a∩κ∈S})\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\diamondsuit_{\kappa,\lambda} : a \cap \kappa \in S\})}$$\end{document} holds. (shrink)

In this thesis, we study transfer principles in the context of certain Henselian valued fields, namely Henselian valued fields of equicharacteristic $0$, algebraically closed valued fields, algebraically maximal Kaplansky valued fields, and unramified mixed characteristic Henselian valued fields with perfect residue field. First, we compute the burden of such a valued field in terms of the burden of its value group and its residue field. The burden is a cardinal related to the model theoretic complexity and a notion of (...) dimension associated to $\text {NTP}_2$ theories. We show, for instance, that the Hahn field $\mathbb {F}_p^{\text {alg}})$ is inp-minimal, and that the ring of Witt vectors $W$ over $\mathbb {F}_p^{\text {alg}}$ is not strong. This result extends previous work by Chernikov and Simon and realizes an important step toward the classification of Henselian valued fields of finite burden. Second, we show a transfer principle for the property that all types realized in a given elementary extension are definable. It can be written as follows: a valued field as above is stably embedded in an elementary extension if and only if its value group is stably embedded in the corresponding extension of value groups, its residue field is stably embedded in the corresponding extension of residue fields, and the extension of valued fields satisfies a certain algebraic condition. We show, for instance, that all types over the power series field $\mathbb {R})$ are definable. Similarly, all types over the quotient field of $W$ are definable. This extends previous work of Cubides and Delon and of Cubides and Ye.These distinct results use a common approach, which has been developed recently. It consists of establishing first a reduction to an intermediate structure called the leading term structure, or $\operatorname {\mathrm {RV}}$ -sort, and then of reducing to the value group and residue field. This leads us to develop similar reduction principles in the context of pure short exact sequences of abelian groups.prepared by Pierre Touchard.E-mail: pierre[email protected]: https://miami.uni-muenster.de/Record/a612cf73-0a2f-42c4-b1e4-7d28934138a9. (shrink)

We study the effects of piece selection principles on cardinal arithmetic (Shelah style). As an application, we discuss questions of Abe and Usuba. In particular, we show that if, then (a) is not (λ, 2)‐distributive, and (b) does not hold.

We show that if κ is an infinite successor cardinal, and λ > κ a cardinal of cofinality less than κ satisfying certain conditions, then no ideal on Pκ is weakly λ+-saturated. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Let$\kappa $be a regular uncountable cardinal, anda cardinal greater than or equal to$\kappa $. Revisiting a celebrated result of Shelah, we show that ifis close to$\kappa $and(= the least size of a cofinal subset of) is greater than, thencan be represented (in the sense of pcf theory) as a pseudopower. This can be used to obtain optimal results concerning the splitting problem. For example we show that ifand, then no$\kappa $-complete ideal onis weakly-saturated.

Drawing upon feminist, queer, and crip phenomenology, this essay argues that the distinct temporality of the lived, stuttering body disturbs the normalized “choreography” of communication and thereby threatens the disabled speaker's recognition as a speaking subject. Examined through the phenomenology of Maurice Merleau-Ponty and Alfred Schutz, the disabled speaking body is temporally “out of step” with the normalized bodily rhythms and pace of communicative practices in relation to both lived and objective time. Disciplined for his incalculable and therefore irrational bodily (...) choreography, the disabled speaker is foregrounded against an objective, instrumentally ordered world constituted by a disembodied and hegemonic “straight-masculine” time. Although dominant communicative choreographies may often be unlivable for disabled speakers, cripping communicative time rejects the cardinal value of futurity and invites interlocutors to gather in a noninstrumentalized and nonproductive present. This reshaping of communicative space enacts new modes of relationality and opens up an array of communicative futures suppressed or cut off by straight-masculine time. (shrink)

Let κ be a regular uncountable cardinal and λ be a cardinal greater than κ. We show that if 2 <κ ≤ M(κ, λ), then ◇ κ,λ holds, where M(κ, λ) equals $\lambda ^{\aleph }0$ if cf(λ) ≥ κ, and $(\lambda ^{+})^{\aleph _{0}}$ otherwise.

We revisit several results concerning club principles and nonsaturation of the nonstationary ideal, attempting to improve them in various ways. So we typically deal with a ideal J extending the nonstationary ideal on a regular uncountable cardinal \, our goal being to witness the nonsaturation of J by the existence of towers ).

Given a regular uncountable cardinal κ and a cardinal λ > κ of cofinality ω, we show that the restriction of the non-stationary ideal on Pκ to the set of all a with equation image is not λ++-saturated . We actually prove the stronger result that there is equation image with |Q| = λ++ such that A∩B is a non-cofinal subset of Pκ for any two distinct members A, B of Q, where NGκ, λ denotes the game ideal (...) on Pκ. We also remark that for κ > ω1, adding λ+3 Cohen subsets of ω1 to equation image makes NGκ, λ λ+3-saturated. (shrink)

Assuming the consistency of the theory “ZFC + there exists a measurable cardinal”, we construct 1. a model in which the first cardinal κ, such that 2κ > κ+, bears a normal filter F whose associated boolean algebra is κ+-distributive ,2. a model where there is a measurable cardinal κ such that, for every regular cardinal ρ < κ, 2ρ = ρ++ holds,3. a model of “ZFC + GCH” where there exists a non-measurable cardinal κ (...) bearing a normal filter F whose associated boolean algebra is κ+-distributive. (shrink)

Using previous work of Baumgartner, Shelah and others, we describe, for each infinite cardinal θκ, the smallest κ-normal ideal J on Pκ such that.

Given a regular infinite cardinal κ and a cardinal λ > κ, we study fine ideals H on Pκ that satisfy the square brackets partition relation equation image, where μ is a cardinal ≥2.

Building upon earlier work of Donna Carr, Don Pelletier, Chris Johnson, Shu-Guo Zhang and others, we show that a normal ideal J on Pκ is strongly normal if and only if J+→< 2 for every μ < κ, and we describe the least normal ideal J on Pκ such that J+ →< 2.

We present a version for κ-distributive ideals over a regular infinite cardinal κ of some of the combinatorial results of Mathias on happy families. We also study an associated notion of forcing, which is a generalization of Mathias forcing and of Prikry forcing.

We use games of Kastanas to obtain a new characterization of the classC ℱ of all sets that are completely Ramsey with respect to a given happy family ℱ. We then combine this with ideas of Plewik to give a uniform proof of various results of Ellentuck, Louveau, Mathias and Milliken concerning the extent ofC ℱ. We also study some cardinals that can be associated with the ideal ℐℱ of nowhere ℱ-Ramsey sets.

We study the degree of (weak) Q-pointness, and that of (weak) P-pointness, of ideals on a regular infinite cardinal.

Given a regular cardinal κ > ω1 and a cardinal λ with κ ≤ cf (λ) < λ, we show that NSκ,λ | T is not λ+-saturated, where T is the set of all \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${a\in P_\kappa (\lambda)}$$\end{document} such that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${| a | = | a \cap \kappa|}$$\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}$${{\rm cf} \big( {\rm (...) sup} (a\cap\kappa)\big) = {\rm cf} \big({\rm sup} (a)\big) = \omega}$$\end{document}. (shrink)

We study the role of meeting numbers in pcf theory. In particular, Shelah's Strong Hypothesis is shown to be equivalent to the assertion that for any singular cardinal σ of cofinality ω, there is a size collection Q of countable subsets of σ with the property that for any infinite subset a of σ, there is a member of Q meeting a in an infinite set.

We give a new characterization of the nonstationary ideal on \\) in the case when \ is a regular uncountable cardinal and \ a singular strong limit cardinal of cofinality at least \.

We study the partition relation $X@>{\rm w}>>[Y]_{p}^{2}$ that is a weakening of the usual partition relation $X\rightarrow [Y]_{p}^{2}$ . Our main result asserts that if κ is an uncountable strongly compact cardinal and $\germ{d}_{\kappa}\leq \lambda ^{<\kappa}$ , then $I_{\kappa,\lambda}^{+}@>{\rm w}>>[I_{\kappa,\lambda}^{+}]_{\lambda <\kappa}^{2}$ does not hold.

Le P. Georges Chantraine s’est lancé dans une impressionnante biogra­phie consacrée à Henri de Lubac. Impressionnante par son ampleur, puisque quatre tomes sont annoncés ! Le premier vient d’être publié, il compte plus de 700 pages. La masse des documents consultés est considérable : toutes les archives du cardinal, bien sûr, mais aussi les documents familiaux, les lettres et les cartes adressées par le jeune Henri à sa famille. Le résultat impres­sionne encore plus par la mise en perspective..

A theory [Formula: see text] is said to have exact saturation at a singular cardinal [Formula: see text] if it has a [Formula: see text]-saturated model which is not [Formula: see text]-saturated. We show, under some set-theoretic assumptions, that any simple theory has exact saturation. Also, an NIP theory has exact saturation if and only if it is not distal. This gives a new characterization of distality.

For every uncountable regular cardinalκ and any cardinalλ≧κ,P κ λ denotes the set $\left\{ {x \subseteqq \lambda :\left| x \right|< \kappa } \right\}$ . Furthermore, < denotes the binary operation defined inP κ λ byx (...) + denotes the setP κ λ−I, andI * the filter dual toI.An idealI overP κ λ is said to benormal iff every functionf:P κ λ→λ with the property that {x∈P κ λ:f(x)∈x}∈I + is constant on a set inI +.I is said to bestrongly normal iff every functionf:P κ λ→P κ λ with the property that {x∈P κ λ:x∩xκ≠Ø∧f(x)shrink)

La dotta ignoranza -- Le congetture -- Il Dio nascosto -- La ricerca di Dio -- La filiazione di Dio -- Il dono del Padre dei lumi -- Congettura sugli ultimi giorni -- Dialogo sulla Genesi -- Difesa della dotta ignoranza -- La sapienza -- La mente -- Gli esperimenti con la bilancia -- La visione di Dio -- Il berillo -- L'ugaglianza -- Il principio -- Il potere che è -- il non-altro -- La caccia della sapienza -- Il (...) gioco della palla -- Compendio -- Il vertice della contemplazione -- La quadratura del cerchio -- I complementi matematici -- La perfezione matematica. (shrink)

Since the 1980s, society's wealthiest members have claimed an ever-expanding share of income and property. It has been a true counterrevolution, says Pierre Rosanvallon--the end of the age of growing equality launched by the American and French revolutions. And just as significant as the social and economic factors driving this contemporary inequality has been a loss of faith in the ideal of equality itself. An ambitious transatlantic history of the struggles that, for two centuries, put political and economic equality (...) at their heart, The Society of Equals calls for a new philosophy of social relations to reenergize egalitarian politics. For eighteenth-century revolutionaries, equality meant understanding human beings as fundamentally alike and then creating universal political and economic rights. Rosanvallon sees the roots of today's crisis in the period 1830-1900, when industrialized capitalism threatened to quash these aspirations. By the early twentieth century, progressive forces had begun to rectify some imbalances of the Gilded Age, and the modern welfare state gradually emerged from Depression-era reforms. But new economic shocks in the 1970s began a slide toward inequality that has only gained momentum in the decades since. There is no returning to the days of the redistributive welfare state, Rosanvallon says. Rather than resort to outdated notions of social solidarity, we must instead revitalize the idea of equality according to principles of singularity, reciprocity, and communality that more accurately reflect today's realities. (shrink)

Written with verve and intensity (and a good bit of wordplay), this is the long-awaited study of Flaubert and the modern literary field that constitutes the ...

Over the past four decades, French sociologist Pierre Bourdieu produced one of the most imaginative and subtle bodies of social theory of the postwar era. When he died in 2002, he was considered to be the most influential sociologist in the world and a thinker on a par with Foucault and Le;vi-Strauss—a public intellectual as important to his generation as Sartre was to his. Sketch for a Self-Analysis is the ultimate outcome of Bourdieu’s lifelong preoccupation with reflexivity. Vehemently not (...) an autobiography, this unique book is instead an application of Bourdieu’s theories to his own life and intellectual trajectory; along the way it offers compelling and intimate insights into the most important French intellectuals of the time—including Foucault, Sartre, Aron, Althusser, and de Beauvoir—as well as Bourdieu’s own formative experiences at boarding school and his moral outrage at the colonial war in Algeria. (shrink)

Bien des difficultés que nous éprouvons à comprendre les oeuvres philosophiques des Anciens proviennent souvent du fait que nous commmettons en les interprétant un double anachronisme: nous croyons que, comme beaucoup d'oeuvres modernes, elles sont destinées à communiquer des informations concernant un contenu conceptuel donné et que nous pouvons aussi en tirer directement des renseignements clairs sur la pensée et la psychologie de leur auteur. Mais en fait, elles sont très souvent des exercices spirituels que l'auteur pratique lui-même et fait (...) pratiquer à son lecteur. Elles sont destinées à former les âmes. Elles ont une valeur psychagogique. (shrink)

Les trois dialogues composés par le cardinal Nicolas de Cues pendant l'été 1450 ne résument pas toute la pensée de cet auteur, mais ils éclairent d'un jour relativement nouveau sa réflexion sur le lien entre sagesse et savoir. Proche en cela des Anciens, Nicolas de Cues pense leur unité dans la lumière de l'Un - de la Déité, écrit-il parfois - réfléchie par la puissance de l'esprit humain. Cet esprit est compris comme imago dei, non pas image de Dieu, (...) car tout ce qui est image de Dieu, mais plutôt copie de Dieu, reprise de la toute-puissance divine dans les limites que lui impose, toutefois, le fait d'être finie. La vérité étant en elle-même inaccessible ici-bas - inattingible, écrit Nicolas de Cues - reste le développement de cette vérité ou de l'Un, c'est à dire ce monde que l'esprit a pour tâche de mesurer, de reprendre, de recréer. Savoir pour inventer un monde à venir, avec humilité et ouverture à l'Etranger : cela s'accorde précisément avec ce que certains historiens nomment l'Humanisme. (shrink)

« La métaphysique d’Aristote n’est, au sens aristotélicien, dialectique et par là incapable de tout achèvement déductif, que parce qu’elle est une métaphysique du mouvement, c’est-à-dire de la scission. » Le propos de l’auteur est simple : sans vouloir rajouter et apporter du nouveau sur Aristote, il tente au contraire de désapprendre tout ce que la tradition a ajouté à l’aristotélisme primitif. Car l’aristotélisme que nous connaissons est surtout celui des commentateurs grecs. L’image ainsi révélée est celle d’un Aristote aporétique, (...) mais « cette voix qui parle est celle plus fraternelle qui continue de chercher en nous ce qu’est l’être et de se taire parfois ». (shrink)

Résumé La localisation des implantations des grands éléments d’infrastructure collective pose des problèmes de légitimation juridique spécifique. Ils délimitent en effet plusieurs territoires distincts en fonction de la nature des impacts qu’ils provoquent, lesquels, chacun, sont soumis à leurs propres législations et rentrent dans les compétences d’autorités différentes, y compris celle dont dépend la décision sur l’infrastructure envisagée. De telles situations normatives complexes empêchent la sémantisation légitimante que le droit est censé assurer dans les décisions de l’appareil étatique: elle sera (...) toujours partielle, voire lacunaire. Les compensations ne peuvent être que procédurales, et celles-ci sont insuffisantes à atteindre l’idéal postulé par le principe de légalité des activités publiques. Mais il ne peut en aller autrement pour ces infrastructures. (shrink)

Tied to the apron strings of the church -- Researcher, teacher, philosopher -- Philosophical discourse -- Interpretation, objectivity and nonsense -- Unitary experience and philosophical life -- Philosophical discourse as spiritual exercise -- Philosophy as life and as a quest for wisdom -- From Socrates to Foucault : a long tradition -- Inacceptable? -- The present alone is our happiness.

Les sociétés contemporaines tendent à ne plus connaître que les réalités individuelles et une perspective générale hors déterminations spécifiées. D'où la mise à l'écart de toute tradition, religieuse ou culturelle, et un refoulement de ce qui les portait. Cet ouvrage entend promouvoir une reconnaissance de la pluralité des voies de l'humain, mais sans juxtaposition communautariste, et préconise la mise en place de conditions de confrontations sur fond de différends fructueux et d'hétérogénéité foncière. C'est peut-être notre seule chance pour l'avènement de (...) chacun et un renouvellement social. Cela passera par des enjeux à faire réapparaître à l'encontre d'insidieuses neutralisations, et requiert des régimes de raison divers mais tous développés suivant un mode de rationalité publique. Sont ici en cause nos identités, nos rapports au passé et nos imaginations d'avenir, ainsi que ce qui nous y mobilise. (shrink)