The Determinacy of Long Games

The Determinacy of Long Games
Author :
Publisher : Walter de Gruyter
Total Pages : 333
Release :
ISBN-10 : 9783110200065
ISBN-13 : 3110200066
Rating : 4/5 (65 Downloads)

Synopsis The Determinacy of Long Games by : Itay Neeman

In this volume the author develops and applies methods for proving, from large cardinals, the determinacy of definable games of countable length on natural numbers. The determinacy is ultimately derived from iteration strategies, connecting games on natural numbers with the specific iteration games that come up in the study of large cardinals. The games considered in this text range in strength, from games of fixed countable length, through games where the length is clocked by natural numbers, to games in which a run is complete when its length is uncountable in an inner model (or a pointclass) relative to the run. More can be done using the methods developed here, reaching determinacy for games of certain length. The book is largely self-contained. Only graduate level knowledge of modern techniques in large cardinals and basic forcing is assumed. Several exercises allow the reader to build on the results in the text, for example connecting them with universally Baire and homogeneously Suslin sets. - Important contribution to one of the main features of current set theory, as initiated and developed by Jensen, Woodin, Steel and others.

The Determinacy of Long Games

The Determinacy of Long Games
Author :
Publisher : Walter de Gruyter
Total Pages : 332
Release :
ISBN-10 : 9783110183412
ISBN-13 : 3110183412
Rating : 4/5 (12 Downloads)

Synopsis The Determinacy of Long Games by : Itay Neeman

Review text: "There is an excellent extensive Introduction presenting a view of the theory that can be profitable for a non-specialist as well."(ap) in: EMS-Newsletter 3/2007.

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)

Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes)
Author :
Publisher : World Scientific
Total Pages : 5393
Release :
ISBN-10 : 9789813272897
ISBN-13 : 9813272899
Rating : 4/5 (97 Downloads)

Synopsis Proceedings Of The International Congress Of Mathematicians 2018 (Icm 2018) (In 4 Volumes) by : Boyan Sirakov

The Proceedings of the ICM publishes the talks, by invited speakers, at the conference organized by the International Mathematical Union every 4 years. It covers several areas of Mathematics and it includes the Fields Medal and Nevanlinna, Gauss and Leelavati Prizes and the Chern Medal laudatios.

The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal

The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal
Author :
Publisher : Walter de Gruyter
Total Pages : 944
Release :
ISBN-10 : 9783110804737
ISBN-13 : 3110804735
Rating : 4/5 (37 Downloads)

Synopsis The Axiom of Determinacy, Forcing Axioms, and the Nonstationary Ideal by : W. Hugh Woodin

The series is devoted to the publication of high-level monographs on all areas of mathematical logic and its applications. It is addressed to advanced students and research mathematicians, and may also serve as a guide for lectures and for seminars at the graduate level.

Ordinal Definability and Recursion Theory

Ordinal Definability and Recursion Theory
Author :
Publisher : Cambridge University Press
Total Pages : 552
Release :
ISBN-10 : 9781107033405
ISBN-13 : 1107033403
Rating : 4/5 (05 Downloads)

Synopsis Ordinal Definability and Recursion Theory by : Alexander S. Kechris

The third in a series of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar'.

The Ultrapower Axiom

The Ultrapower Axiom
Author :
Publisher : Walter de Gruyter GmbH & Co KG
Total Pages : 325
Release :
ISBN-10 : 9783110719734
ISBN-13 : 3110719738
Rating : 4/5 (34 Downloads)

Synopsis The Ultrapower Axiom by : Gabriel Goldberg

The book is about strong axioms of infinity (also known as large cardinal axioms) in set theory, and the ongoing search for natural models of these axioms. Assuming the Ultrapower Axiom, we solve various classical problems in set theory (e.g., the Generalized Continuum Hypothesis) and develop a theory of large cardinals that is much clearer than the theory that can be developed using only the standard axioms.

Set Theory

Set Theory
Author :
Publisher : Springer
Total Pages : 335
Release :
ISBN-10 : 9783319067254
ISBN-13 : 3319067257
Rating : 4/5 (54 Downloads)

Synopsis Set Theory by : Ralf Schindler

This textbook gives an introduction to axiomatic set theory and examines the prominent questions that are relevant in current research in a manner that is accessible to students. Its main theme is the interplay of large cardinals, inner models, forcing and descriptive set theory. The following topics are covered: • Forcing and constructability • The Solovay-Shelah Theorem i.e. the equiconsistency of ‘every set of reals is Lebesgue measurable’ with one inaccessible cardinal • Fine structure theory and a modern approach to sharps • Jensen’s Covering Lemma • The equivalence of analytic determinacy with sharps • The theory of extenders and iteration trees • A proof of projective determinacy from Woodin cardinals. Set Theory requires only a basic knowledge of mathematical logic and will be suitable for advanced students and researchers.

Interpreting Gödel

Interpreting Gödel
Author :
Publisher : Cambridge University Press
Total Pages : 293
Release :
ISBN-10 : 9781139991759
ISBN-13 : 1139991752
Rating : 4/5 (59 Downloads)

Synopsis Interpreting Gödel by : Juliette Kennedy

The logician Kurt Gödel (1906–1978) published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Gödel's work on the foundations and philosophy of mathematics. Their essays explore almost every aspect of Godel's intellectual legacy including his concepts of intuition and analyticity, the Completeness Theorem, the set-theoretic multiverse, and the state of mathematical logic today. This groundbreaking volume will be invaluable to students, historians, logicians and philosophers of mathematics who wish to understand the current thinking on these issues.

Sets and Extensions in the Twentieth Century

Sets and Extensions in the Twentieth Century
Author :
Publisher : Elsevier
Total Pages : 878
Release :
ISBN-10 : 9780080930664
ISBN-13 : 0080930662
Rating : 4/5 (64 Downloads)

Synopsis Sets and Extensions in the Twentieth Century by :

Set theory is an autonomous and sophisticated field of mathematics that is extremely successful at analyzing mathematical propositions and gauging their consistency strength. It is as a field of mathematics that both proceeds with its own internal questions and is capable of contextualizing over a broad range, which makes set theory an intriguing and highly distinctive subject. This handbook covers the rich history of scientific turning points in set theory, providing fresh insights and points of view. Written by leading researchers in the field, both this volume and the Handbook as a whole are definitive reference tools for senior undergraduates, graduate students and researchers in mathematics, the history of philosophy, and any discipline such as computer science, cognitive psychology, and artificial intelligence, for whom the historical background of his or her work is a salient consideration - Serves as a singular contribution to the intellectual history of the 20th century - Contains the latest scholarly discoveries and interpretative insights

Large Cardinals, Determinacy and Other Topics

Large Cardinals, Determinacy and Other Topics
Author :
Publisher : Cambridge University Press
Total Pages : 317
Release :
ISBN-10 : 9781107182998
ISBN-13 : 1107182999
Rating : 4/5 (98 Downloads)

Synopsis Large Cardinals, Determinacy and Other Topics by : Alexander S. Kechris

The final volume in a series of four books presenting the seminal papers from the Caltech-UCLA 'Cabal Seminar'.