Extensions Of The Axiom Of Determinacy
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Extensions Of The Axiom Of Determinacy
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Author : Paul B. Larson
language : en
Publisher: American Mathematical Society
Release Date : 2023-10-19
Extensions Of The Axiom Of Determinacy written by Paul B. Larson and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-19 with Mathematics categories.
This is an expository account of work on strong forms of the Axiom of Determinacy (AD) by a group of set theorists in Southern California, in particular by W. Hugh Woodin. The first half of the book reviews necessary background material, including the Moschovakis Coding Lemma, the existence of strong partition cardinals, and the analysis of pointclasses in models of determinacy. The second half of the book introduces Woodin's axiom system $mathrm{AD}^{+}$ and presents his initial analysis of these axioms. These results include the consistency of $mathrm{AD}^{+}$ from the consistency of AD, and its local character and initial motivation. Proofs are given of fundamental results by Woodin, Martin, and Becker on the relationships among AD, $mathrm{AD}^{+}$, the Axiom of Real Determinacy, and the Suslin property. Many of these results are proved in print here for the first time. The book briefly discusses later work and fundamental questions which remain open. The study of models of $mathrm{AD}^{+}$ is an active area of contemporary research in set theory. The presentation is aimed at readers with a background in basic set theory, including forcing and ultrapowers. Some familiarity with classical results on regularity properties for sets of reals under AD is also expected.
The Axiom Of Determinacy Forcing Axioms And The Nonstationary Ideal
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Author : W. Hugh Woodin
language : en
Publisher: Walter de Gruyter
Release Date : 2010
The Axiom Of Determinacy Forcing Axioms And The Nonstationary Ideal written by W. Hugh Woodin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This is the revised edition of a well-established monograph on the identification of a canonical model in which the Continuum Hypothesis is false. Written by an expert in the field, it is directed to researchers and advanced graduate students in Mat
Measure Theory
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Author : Vladimir I. Bogachev
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-15
Measure Theory written by Vladimir I. Bogachev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-15 with Mathematics categories.
This book giving an exposition of the foundations of modern measure theory offers three levels of presentation: a standard university graduate course, an advanced study containing some complements to the basic course, and, finally, more specialized topics partly covered by more than 850 exercises with detailed hints and references. Bibliographical comments and an extensive bibliography with 2000 works covering more than a century are provided.
General Topology Under The Axiom Of Determinacy
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Author : Apollo Francis Hogan
language : en
Publisher:
Release Date : 2004
General Topology Under The Axiom Of Determinacy written by Apollo Francis Hogan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
Higher Recursion Theory And Set Theory
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Author : James Cummings
language : en
Publisher: World Scientific
Release Date : 2025-02-18
Higher Recursion Theory And Set Theory written by James Cummings and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-18 with Mathematics categories.
This volume celebrates the research contributions of Professors Theodore A Slaman and W Hugh Woodin, marking their distinguished careers in higher recursion theory and set theory as they approached the milestone of their 65th birthdays in 2019. It originates from the Institute for Mathematical Sciences program, Higher Recursion Theory and Set Theory, held at the National University of Singapore (May 20-June 14, 2019).The program explored cutting-edge developments in higher recursion theory, set theory, and their intricate interconnections. Topics discussed during the workshop included Martin's conjecture, higher randomness, the HOD conjecture, descriptive inner model theory, and the Ultimate-L program.This volume presents 15 peer-reviewed contributions by leading experts in the field, offering a comprehensive overview of recent advances in higher recursion theory and set theory, with a focus on their dynamic interactions.
Sets And Extensions In The Twentieth Century
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Author :
language : en
Publisher: Elsevier
Release Date : 2012-01-24
Sets And Extensions In The Twentieth Century written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-24 with Mathematics categories.
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
Logic And Its Applications
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Author : Mohua Banerjee
language : en
Publisher: Springer Nature
Release Date : 2023-02-22
Logic And Its Applications written by Mohua Banerjee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-22 with Mathematics categories.
Edited in collaboration with FoLLI, this book constitutes the refereed proceedings of the 10th Indian Conference on Logic and Its Applications, ICLA 2023, which was held in Indore, India, in March 2023. Besides 6 invited papers presented in this volume, there are 9 contributed full papers which were carefully reviewed and selected from 18 submissions. The volume covers a wide range of topics. These topics are related to modal and temporal logics, intuitionistic connexive and imperative logics, systems for reasoning with vagueness and rough concepts, topological quasi-Boolean logic and quasi-Boolean based rough set models, and first-order definability of path functions of graphs.
Handbook Of Set Theory
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Author : Matthew Foreman
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-10
Handbook Of Set Theory written by Matthew Foreman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-10 with Mathematics categories.
Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to put geometry on a ?rm footing. With roots in the Elements, the distinctive methodology of mathematics has become proof. Inevitably two questions arise: What are proofs? and What assumptions are proofs based on? The ?rst question, traditionally an internal question of the ?eld of logic, was also wrestled with in antiquity. Aristotle gave his famous syllogistic s- tems, and the Stoics had a nascent propositional logic. This study continued with ?ts and starts, through Boethius, the Arabs and the medieval logicians in Paris and London. The early germs of logic emerged in the context of philosophy and theology. The development of analytic geometry, as exempli?ed by Descartes, ill- tratedoneofthedi?cultiesinherentinfoundingmathematics. Itisclassically phrased as the question ofhow one reconciles the arithmetic with the geom- ric. Arenumbers onetypeofthingand geometricobjectsanother? Whatare the relationships between these two types of objects? How can they interact? Discovery of new types of mathematical objects, such as imaginary numbers and, much later, formal objects such as free groups and formal power series make the problem of ?nding a common playing ?eld for all of mathematics importunate. Several pressures made foundational issues urgent in the 19th century.
Logical Foundations Of Mathematics And Computational Complexity
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Author : Pavel Pudlák
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-22
Logical Foundations Of Mathematics And Computational Complexity written by Pavel Pudlák and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
The two main themes of this book, logic and complexity, are both essential for understanding the main problems about the foundations of mathematics. Logical Foundations of Mathematics and Computational Complexity covers a broad spectrum of results in logic and set theory that are relevant to the foundations, as well as the results in computational complexity and the interdisciplinary area of proof complexity. The author presents his ideas on how these areas are connected, what are the most fundamental problems and how they should be approached. In particular, he argues that complexity is as important for foundations as are the more traditional concepts of computability and provability. Emphasis is on explaining the essence of concepts and the ideas of proofs, rather than presenting precise formal statements and full proofs. Each section starts with concepts and results easily explained, and gradually proceeds to more difficult ones. The notes after each section present some formal definitions, theorems and proofs. Logical Foundations of Mathematics and Computational Complexity is aimed at graduate students of all fields of mathematics who are interested in logic, complexity and foundations. It will also be of interest for both physicists and philosophers who are curious to learn the basics of logic and complexity theory.
The Axiom Of Choice
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Author : Thomas J. Jech
language : en
Publisher: Courier Corporation
Release Date : 2008-01-01
The Axiom Of Choice written by Thomas J. Jech and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-01 with Mathematics categories.
Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.