The purpose of this paper is to outline some recent progress in descriptive inner model theory, a branch of set theory which studies descriptive set theoretic and inner model theoretic objects using tools from both areas. There are several interlaced problems that lie on the border of these two areas of set theory, but one that has been rather central for almost two decades is the conjecture known as the Mouse Set Conjecture. One particular motivation for resolving MSC is that (...) it provides grounds for solving the inner model problem which dates back to 1960s. There have been some new partial results on MSC and the methods used to prove the new instances suggest a general program for solving the full conjecture. It is then our goal to communicate the ideas of this program to the community at large. (shrink)

Building on the work of Schimmerling [Coherent sequences and threads, Adv. Math.216 89–117] and Steel [PFA implies AD L, J. Symbolic Logic70 1255–1296], we show that the failure of square principle at a singular strong limit cardinal implies that there is a nontame mouse. The proof presented is the first inductive step beyond L of the core model induction that is aimed at getting a model of ADℝ + "Θ is regular" from the failure of square at a singular strong (...) limit cardinal or PFA. (shrink)

Frege’s famous definition of number famously uses the concept of “extension”. Extensions, in the Fregean framework, are susceptible to bringing many difficulties, and, some say, even paradoxes. Therefore, neo-logicist programs want to avoid the problems and to replace the classical Fregean definition of number with Hume’s Principle. I argue that this move, even if it makes sense from a computational point of view, is at odds with Frege’s larger philosophical project. For Frege, I claim, extensions were an important part of (...) his philosophical program of logic-as-an-universal-language. This is why Frege places his project in line with Leibniz’ philosophical project of finding a lingua characterica universalis. (shrink)

Frege’s famous definition of number famously uses the concept of “extension”. Extensions, in the Fregean framework, are susceptible to bringing many difficulties, and, some say, even paradoxes. Therefore, neo-logicist programs want to avoid the problems and to replace the classical Fregean definition of number with Hume’s Principle. I argue that this move, even if it makes sense from a computational point of view, is at odds with Frege’s larger philosophical project. For Frege, I claim, extensions were an important part of (...) his philosophical program of logic-as-an-universal-language. This is why Frege places his project in line with Leibniz’ philosophical project of finding a lingua characterica universalis. (shrink)

Frege’s famous definition of number famously uses the concept of “extension”. Extensions, in the Fregean framework, are susceptible to bringing many difficulties, and, some say, even paradoxes. Therefore, neo-logicist programs want to avoid the problems and to replace the classical Fregean definition of number with Hume’s Principle. I argue that this move, even if it makes sense from a computational point of view, is at odds with Frege’s larger philosophical project. For Frege, I claim, extensions were an important part of (...) his philosophical program of logic-as-an-universal-language. This is why Frege places his project in line with Leibniz’ philosophical project of finding a lingua characterica universalis. (shrink)

I analyze in this article the different ways in which Descartes uses abstraction in the Regulæ, discussing his project of a mathematical physics, the role of the imagination, and the status of numbers. I also try to show that the doctrine of simple natures cannot be well accommodated with the theory of abstraction developed in Rule 14, having instead a greater affinity with Descartes’ later theory of abstraction and exclusion, in which imagination plays no role and everything happens at a (...) strictly intellectual level. This interpretation is supported by the recent discovery of the Cambridge manuscript, which almost certainly records an early stage of composition and in which the doctrine of simple natures is absent, thus being very probably a later development. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:BOOK REVIEWS 187 standing. He picks his way philosophicelly ~darough the many preludes, interludes and epilogues of the long, autobiographical poem, The Prelude. He succeeds in interpreting philosophically.Wordsworth's absorption in "the life of things" and the "immanence of the world soul." These ideas remain, it seems to me, in Wordsworth's mind as well as in.his art primarily "lyrical ballads." But Melvin Rader has given us a thoroughly intelligible account, (...) both historical and philosophical, of both Coleridge and Wordsworth as reflectiveminds, without detracting item them as artists. HERBERTW. SCHNEIDER Claremont Graduate School and Unlver~i~y Center gchelting et la R~alit~ Finis: Essai sur la Philosophic de la Nature et de l'[dentit~. By Judith E. Schlanger. (Paris: Presses Universitaires de France, 1966. Pp. 162. = Biblioth~que de Philosophie Contemporaine: Histoire de ta Philosophie et Philosophie Gfin6rale. Paper, F. 12.--) L'dtude de Judith E. Schlanger pr~se~te un bref expos6 des th~mes princ~paux de la pens~e philosophlque de Schelling en retra~ant de fa~on plus ou moius syst6matique l'itindraire spirituel de ce grand penseur qui a crd6 les fondsments spdculatifs du romantisme aIlemand. La philosophie de Schelling refl~te une ardeur,constants de recherche toujours progressive miroitant lea rythmes intimes de son articulation/~ la fois subtile et intensive. Nous allons donner en raccourci la principale ligne d'6volution de cette pens~e. L'essai de Schlanger a pour objet propre le probl~me philosophique qui rdsulte de la connexion 6troite de deux th~mes constituant les fondoments de la philosophie schellingienne, notamment le bh6me d'une philosophie concrAte qui rdcupAre intdgralement l'intuition et celui de la simultan6it6 de l'absolu et du finidans une rdalitdqui n'est constitu6e que par des totas diserAtes. Pour Schelling l'absolu n'est autre chose que la rdalitd concrete constitude par l'ensemble des totalitds individuelles et particuli6res qui sent con~ues comme dtant organiques et qui sent intelligibles, c'est-~.dire leur prdsence et leur raison d'etre coincident et ne peuvent ~tre saisiesque par l'immddiatetd de l'intuition intellectuelle et non par une rationslitd ddductive. L'absolu eat organicitd intelligibleau moyen d'un mode de connaissance intdgralement intuitif, done de rationalitd/t dvidence pleine et non de rationalitd ~t mddiation conceptuelle. L'absolu est done un total, une totalitd complexe ~ cause do ses articulations ind6finiment multiples ~tl'intdrieur. La philosophie enest la transposition aussi bien dans son d6veloppement actuel que dans l'embrassement des multiples ddterminations en un totalitarisme du savoir. L'instrument opdrationnel et cognitif capable d'61aborer cette transposition est l'intuition,la "Anschauung". En effet l'intuition joue un r61e capital dans la philosophie de Schelling. Issue directement de l'exp6rience sensible, c'est-~-dire, concrbte et individuelle, ellepermet d'englober dans l'immddiatetd d'une seule dvidence ~ la fois coner ~te et totale la coprdsence et la contemporandit6 de l'absolu et du finien une unit6 positive, non-dialectique, mais organique. Il est vrai que le scheme de l'organisme et de l'organicitd detains la pensde de ScheUing. L'absolu et le finisent en correlation organique. L'actualit6 dvidents de leur opposition manifeste leur copr~ence simultande, ce qui traduit leur unit~ absolue, sous-jacente qui a rendu possible cette opposition. La liaison effective, rdelle,empiriquement constatde des deux termes opposds leur suppose un fondement commun absolu. La dichotomie n'estpas primordiale, l'antith~sea pour support affirmatifun absolu. L'absolu est le lieu de l'identitd des opposds. C'est la coincidence immddiate entre des termes antinomiques qui d6finitl'unitd absolue. Et de cet absolu, la philosophic poss~de un savoir imm6diat, c'est-~dire absolu. II en rdsulte que l'intuitionest le principe m~me de l'intelligibilitd.Le probIAme phUosophique capital qui se pose et que Schlanger dtudie dana l'ceuvre de Schelling depuis les ddbuts de sa pensde en 1794jusqu'au moment o~1la philosophie de l'Identitd eat constitude, en 1804environ s'dnonce comme suit: La vision de l'identit6 immddiate des opposds comme forme de la rdalitd absolue pourra-t-elle s'articuler dans un savoir systdmatique et objective- 188 HISTORY OF PHILOSOPHY ment communicable de la totalit6... (shrink)

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

We investigate the indestructibility properties of strongly compact cardinals in universes where strong compactness suffers from identity crisis. We construct an iterative poset that can be used to establish Kimchi–Magidor theorem from (in The independence between the concepts of compactness and supercompactness, circulated manuscript), i.e., that the first n strongly compact cardinals can be the first n measurable cardinals. As an application, we show that the first n strongly compact cardinals can be the first n measurable cardinals while the strong (...) compactness of each strongly compact cardinal is indestructible under Levy collapses (our theorem is actually more general, see Sect. 3). A further application is that the class of strong cardinals can be nonempty yet coincide with the class of strongly compact cardinals while strong compactness of any strongly compact cardinal κ is indestructible under κ-directed closed posets that force GCH at κ. (shrink)

During his Fall 2005 set theory seminar, Woodin asked whether V-supercompactness implies HOD-supercompactness. We show, as he predicted, that that the answer is no.

Many have argued against the claim that Plato posited the mathematical objects that are the subjects of Metaphysics M and N. This paper shifts the burden of proof onto these objectors to show that Plato did not posit these entities. It does so by making two claims: first, that Plato should posit the mathematical Intermediates because Forms and physical objects are ill suited in comparison to Intermediates to serve as the objects of mathematics; second, that their utility, combined with Aristotle’s (...) commentary on Plato’s posit of Intermediates, provides good reason to conclude that Plato did posit them. (shrink)

The third millennium set new requirements for the Orthodox Church, the decision of which depends on its role and place in the future. The question is whether the Church will be really catholic, universal or remain purely local. New demands of a modern man put Orthodoxy in a dilemma - whether to preserve traditionally conservative status, but whether to go through the adaptation of believers and to the requirements of modern times, as it did, for example, the Roman Catholic Church.

Assuming $V=L+AD$, using methods from inner model theory, we give a new proof of the strong partition property for ${\sim}{ \delta }^{2}_{1}$. The result was originally proved by Kechris et al.

We re-prove Becker’s theorem from Becker :229–234, 1981) by showing that \}\) implies that \\vDash ``\omega _2\) is -supercompact”. Our proof uses inner model theoretic tools instead of Baire category. We also show that \ is \-strongly compact.

A set of reals is universally Baire if all of its continuous preimages in topological spaces have the Baire property. ${\sf Sealing}$ is a type of generic absoluteness condition introduced by Woodin that asserts in strong terms that the theory of the universally Baire sets cannot be changed by set forcings. The ${\sf Largest\ Suslin\ Axiom}$ is a determinacy axiom isolated by Woodin. It asserts that the largest Suslin cardinal is inaccessible for ordinal definable surjections. Let ${\sf LSA}$ - ${\sf (...) over}$ - ${\sf uB}$ be the statement that in all generic extensions there is a model of $\sf {LSA}$ whose Suslin, co-Suslin sets are the universally Baire sets. We outline the proof that over some mild large cardinal theory, $\sf {Sealing}$ is equiconsistent with $\sf {LSA}$ - $\sf {over}$ - $\sf {uB}$. In fact, we isolate an exact theory that is equiconsistent with both. As a consequence, we obtain that $\sf {Sealing}$ is weaker than the theory “ $\sf {ZFC}$ + there is a Woodin cardinal which is a limit of Woodin cardinals.” This significantly improves upon the earlier consistency proof of $\sf {Sealing}$ by Woodin. A variation of $\sf {Sealing}$, called $\sf {Tower \ Sealing}$, is also shown to be equiconsistent with $\sf {Sealing}$ over the same large cardinal theory. We also outline the proof that if V has a proper class of Woodin cardinals, a strong cardinal, and a generically universally Baire iteration strategy, then $\sf {Sealing}$ holds after collapsing the successor of the least strong cardinal to be countable. This result is complementary to the aforementioned equiconsistency result, where it is shown that $\sf {Sealing}$ holds in a generic extension of a certain minimal universe. This theorem is more general in that no minimal assumption is needed. A corollary of this is that $\sf {LSA}$ - $\sf {over}$ - $\sf {uB}$ is not equivalent to $\sf {Sealing}$. (shrink)

This book presents the “pleasure phenomenon” as the most important factor in individual and socio-cultural development. This study emphasizes the necessity of transformation of marketing in the 21st Century which would shift the focus from seeking pleasure to controlling desires in a way that would benefit self and society.

In this paper, we show that the failure of the unique branch hypothesis for tame iteration trees implies that in some homogenous generic extension of [Formula: see text] there is a transitive model [Formula: see text] containing [Formula: see text] such that [Formula: see text] is regular. The results of this paper significantly extend earlier works from [Non-tame mice from tame failures of the unique branch bypothesis, Canadian J. Math. 66 903–923; Core models with more Woodin cardinals, J. Symbolic Logic (...) 67 1197–1226] for tame trees. (shrink)

Предназначено для студентов художественных вузов и факультетов, а также для учащихся профессиональных учебных заведений художественного профиля.

kn. 1. Predystorii͡a, zasedanii͡a -- kn. 2. Khronika, portrety.

La question identitaire est un enjeu discret, mais persistant des littératures africaines coloniales et postcoloniales. C’est elle que Lumières de Pointe-Noire d’Alain Mabanckou voudrait interroger à travers les nombreuses stratégies scripturales qu’elle met en jeu. Cette œuvre littéraire caractérisée par l’intergénéricité et l’interartialité apparaît comme un roman n’zassa, ce type d’écrit qui rassemble harmonieusement des genres littéraires et des arts aux formes, poétiques et fonctions différentes. Par cette pratique littéraire de la polyphonie générique et artiale, ce roman traduit, en réalité, (...) le cosmopolitisme de son auteur et, par extension, celui des Africains du continent et de la diaspora, une identité qui fluctue entre afropolitanisme et afropéanisme. (shrink)