We present a question about Suslin trees and the weak square hierarchy which was contributed to the list of open problems of the BIRS workshop.

We study the fine structure of the core model for one Woodin cardinal, building of the work of Mitchell and Steel on inner models of the form . We generalize to some combinatorial principles that were shown by Jensen to hold in L. We show that satisfies the statement: “□κ holds whenever κ the least measurable cardinal λ of order λ++”. We introduce a hierarchy of combinatorial principles □κ, λ for 1 λ κ such that □κ□κ, 1 □κ, λ □κ, (...) κ□κ*. We prove that if holds in V. As an application, we show that ZFC + PFA Con. We also obtain one Woodin cardinal as a lower bound on the consistency strength of stationary reflection at κ+ for a singular, countably closed limit cardinal κ such that # exists; likewise for the failure of □κ* at such a κ. (shrink)

We prove that in all Mitchell-Steel core models, □ κ holds for all κ. (See Theorem 2.). From this we obtain new consistency strength lower bounds for the failure of □ κ if κ is either singular and countably closed, weakly compact, or measurable. (Corallaries 5, 8, and 9.) Jensen introduced a large cardinal property that we call subcompactness; it lies between superstrength and supercompactness in the large cardinal hierarchy. We prove that in all Jensen core models, □ κ holds (...) iff κ is not subcompact. (See Theorem 15; the only if direction is essentially due to Jensen.). (shrink)

We present a general construction of a □κ-sequence in Jensen's fine structural extender models. This construction yields a local definition of a canonical □κ-sequence as well as a characterization of those cardinals κ, for which the principle □κ fails. Such cardinals are called subcompact and can be described in terms of elementary embeddings. Our construction is carried out abstractly, making use only of a few fine structural properties of levels of the model, such as solidity and condensation.

We define what it means for a function on ω1 to be a collapsing function for λ and show that if there exists a collapsing function for +, then there is no precipitous ideal on ω1. We show that a collapsing function for ω2 can be added by forcing. We define what it means to be a weakly ω1-Erdös cardinal and show that in L[E], there is a collapsing function for λ iff λ is less than the least weakly ω1-Erdös (...) cardinal. As a corollary to our results and a theorem of Neeman, the existence of a Woodin limit of Woodin cardinals does not imply the existence of precipitous ideals on ω1. We also show that the following statements hold in L[E]. The least cardinal λ with the Chang property ↠ is equal to the least ω1-Erdös cardinal. In particular, if j is a generic elementary embedding that arises from non-stationary tower forcing up to a Woodin cardinal, then the minimum possible value of j is the least ω1-Erdös cardinal. (shrink)

We show that either of the following hypotheses imply that there is an inner model with a proper class of strong cardinals and a proper class of Woodin cardinals. 1) There is a countably closed cardinal k ≥ N₃ such that □k and □(k) fail. 2) There is a cardinal k such that k is weakly compact in the generic extension by Col(k, k⁺). Of special interest is 1) with k = N₃ since it follows from PFA by theorems of (...) Todorcevic and Velickovic. Our main new technical result, which is due to the first author, is a weak covering theorem for the model obtained by stacking mice over $K^c ||k.$. (shrink)

We prove that if image is a Jensen extender model, then image satisfies the Gap-1 morass principle. As a corollary to this and a theorem of Jensen, the model image satisfies the Gap-2 Cardinal Transfer Property → for all infinite cardinals κ and λ.

We prove that the following two statements are equiconsistent: there exists a greatly Mahlo cardinal; there exists a regular uncountable cardinal κ such that no stationary subset of κ+ ∩ cof carries a partial square.

It is obvious that ♦ implies the existence of an antichain of stationary sets of cardinality which is the largest possible cardinality. We show that the obvious antichain is not maximal and find a less obvious extension of it by ℵ2 more stationary sets.

We introduce the weak partial square principles View the MathML source and View the MathML source, which combine the ideas of a weak square sequence and a partial square sequence. We construct models in which weak partial square principles fail. The main result of the paper is that □λ,κ does not imply View the MathML source.

We consider various quotients of the C*-algebra of bounded operators on a nonseparable Hilbert space, and prove in some cases that, assuming some restriction of the Generalized Continuum Hypothesis, there are many outer automorphisms.

We prove new upper bound theorems on the consistency strengths of SPFA (θ), SPFA(θ-linked) and SPFA(θ⁺-cc). Our results are in terms of (θ, Γ)-subcompactness, which is a new large cardinal notion that combines the ideas behind subcompactness and Γ-indescribability. Our upper bound for SPFA(c-linked) has a corresponding lower bound, which is due to Neeman and appears in his follow-up to this paper. As a corollary, SPFA(c-linked) and PFA(c-linked) are each equiconsistent with the existence of a $\Sigma _{1}^{2}$ -indescribable cardinal. Our (...) upper bound for SPFA(c-c.c.) is a $\Sigma _{2}^{2}$ -indescribable cardinal, which is consistent with V = L. Our upper bound for SPFA(c⁺-linked) is a cardinal κ that is $(\kappa ^{+},\Sigma _{1}^{2})$ -subcompact, which is strictly weaker than κ⁺-supercompact. The axiom MM(c) is a consequence of SPFA(c⁺-linked) by a slight refinement of a theorem of Shelah. Our upper bound for SPFA(c⁺⁺-c.c.) is a cardinal κ that is $(\kappa ^{+},\Sigma _{2}^{2})$ -subcompact, which is also strictly weaker than κ⁺-supercompact. (shrink)

Assume that there is no transitive class model of [Formula: see text] with a Woodin cardinal. Let [Formula: see text] be a singular ordinal such that [Formula: see text] and [Formula: see text]. Suppose [Formula: see text] is a regular cardinal in K. Then [Formula: see text] is a measurable cardinal in K. Moreover, if [Formula: see text], then [Formula: see text].

A Virtue Epistemology presents a new approach to some of the oldest and most gripping problems of philosophy, those of knowledge and scepticism. Ernest Sosa argues for two levels of knowledge, the animal and the reflective, each viewed as a distinctive human accomplishment. By adopting a kind of virtue epistemology in line with the tradition found in Aristotle, Aquinas, Reid, and especially Descartes, he presents an account of knowledge which can be used to shed light on different varieties of (...) scepticism, the nature and status of intuitions, and epistemic normativity. (shrink)

This volume presents a selection of the most influential recent discussions of the crucial metaphysical question: What is it for one event to cause another? The subject of causation bears on many topics, such as time, explanation, mental states, the laws of nature, and the philosophy of science. Contributors include J.L Mackie, Michael Scriven, Jaegwon Kim, G.E.M. Anscombe, G.H. von Wright, C.J. Ducasse, Wesley C. Salmon, David Lewis, Paul Horwich, Jonathan Bennett, Ernest Sosa, and Michael Tooley.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in (...) the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. (shrink)

This paper presents an account of intuitions, and a defense of their epistemic efficacy in general, and more specifically in philosophy, followed by replies in response to various objections.

Thoroughly updated, the second edition of this highly successful textbook continues to represent the most comprehensive and authoritative collection of canonical readings in metaphysics. In addition to updated material from the first edition, it presents entirely new sections on ontology and the metaphysics of material objects. One of the most comprehensive and authoritative metaphysics anthologies available - now updated and expanded Offers the most important contemporary works on the central issues of metaphysics Includes new sections on ontology and the metaphysics (...) of material objects, as well as readings on the topics of fictionalism, fundamentality, tropes, vague identity, temporary intrinsics, stage theory, and composition Surpasses other anthologies in its combination of contributions from leading metaphysicians and a younger generation of "rising-stars". (shrink)

This chapter reviews the major contributions of Donald Davidson to philosophy in the 20th century.

The Politics is one of the most influential texts in the history of political thought, and it raises issues which still confront anyone who wants to think seriously about the ways in which human societies are organized and governed. By examining the way societies are run--from households to city states--Aristotle establishes how successful constitutions can best be initiated and upheld. For this edition, Sir Ernest Barker's fine translation, which has been widely used for nearly half a century, has been (...) extensively revised to meet the needs of the modern reader. The accessible introduction and clear notes examine the historical and philosophical background of the work and discuss its significance for modern political thought. (shrink)

This chapter contains sections titled: Notes and References.

Ernest Gellner's final book, first published in 1998, is a synoptic interpretation of the thought of Wittgenstein and Malinowski.

Philosophical Papers, Volume 40, Issue 3, Page 341-358, November 2011.

Private law governs our most pervasive relationships with other people: the wrongs we do to one another, the property we own and exclude from others' use, the contracts we make and break, and the benefits realized at another's expense that we cannot justly retain. The major rules of private law are well known, but how they are organized, explained, and justified is a matter of fierce debate by lawyers, economists, and philosophers.

PREFACE HERE are many people in America and Europe who want toknow what yoga is, and they say, "Do not tell us about the yoga of one particular school; ...