The Core Model Iterability Problem

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The Core Model Iterability Problem

Author : John R. Steel
Publisher : Cambridge University Press
ISBN 13 : 1316739287
Total Pages : 120 pages
Book Rating : 4.3/5 (167 download)

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Book Synopsis The Core Model Iterability Problem by : John R. Steel

Download or read book The Core Model Iterability Problem written by John R. Steel and published by Cambridge University Press. This book was released on 2017-03-02 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. Large cardinal hypotheses play a central role in modern set theory. One important way to understand such hypotheses is to construct concrete, minimal universes, or 'core models', satisfying them. Since Gödel's pioneering work on the universe of constructible sets, several larger core models satisfying stronger hypotheses have been constructed, and these have proved quite useful. In this volume, the eighth publication in the Lecture Notes in Logic series, Steel extends this theory so that it can produce core models having Woodin cardinals, a large cardinal hypothesis that is the focus of much current research. The book is intended for advanced graduate students and researchers in set theory.

The Core Model Iterability Problem

Author : John R. Steel
Publisher : Cambridge University Press
ISBN 13 : 1107167965
Total Pages : 119 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis The Core Model Iterability Problem by : John R. Steel

Download or read book The Core Model Iterability Problem written by John R. Steel and published by Cambridge University Press. This book was released on 2017-03-02 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suitable for graduate students and researchers in set theory, this volume develops a method for constructing core models that have Woodin cardinals.

Handbook of Set Theory

Author : Matthew Foreman
Publisher : Springer Science & Business Media
ISBN 13 : 1402057644
Total Pages : 2200 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Handbook of Set Theory by : Matthew Foreman

Download or read book Handbook of Set Theory written by Matthew Foreman and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 2200 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fine Structure and Iteration Trees

Author : William J. Mitchell
Publisher : Cambridge University Press
ISBN 13 : 1316763854
Total Pages : 138 pages
Book Rating : 4.3/5 (167 download)

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Book Synopsis Fine Structure and Iteration Trees by : William J. Mitchell

Download or read book Fine Structure and Iteration Trees written by William J. Mitchell and published by Cambridge University Press. This book was released on 2017-03-02 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the third publication in the Lecture Notes in Logic series, Mitchell and Steel construct an inner model with a Woodin cardinal and develop its fine structure theory. This work builds upon the existing theory of a model of the form L[E], where E is a coherent sequence of extenders, and relies upon the fine structure theory of L[E] models with strong cardinals, and the theory of iteration trees and 'backgrounded' L[E] models with Woodin cardinals. This work is what results when fine structure meets iteration trees.

Set Theory of the Continuum

Author : Haim Judah
Publisher : Springer Science & Business Media
ISBN 13 : 1461397545
Total Pages : 417 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Set Theory of the Continuum by : Haim Judah

Download or read book Set Theory of the Continuum written by Haim Judah and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin.

Sets and Proofs

Author : S. Barry Cooper
Publisher : Cambridge University Press
ISBN 13 : 9780521635493
Total Pages : 450 pages
Book Rating : 4.6/5 (354 download)

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Book Synopsis Sets and Proofs by : S. Barry Cooper

Download or read book Sets and Proofs written by S. Barry Cooper and published by Cambridge University Press. This book was released on 1999-06-17 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: First of two volumes providing a comprehensive guide to mathematical logic.

Sets and Extensions in the Twentieth Century

Author :
Publisher : Elsevier
ISBN 13 : 0080930662
Total Pages : 878 pages
Book Rating : 4.0/5 (89 download)

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Book Synopsis Sets and Extensions in the Twentieth Century by :

Download or read book Sets and Extensions in the Twentieth Century written by and published by Elsevier. This book was released on 2012-01-24 with total page 878 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

A Comparison Process for Mouse Pairs

Author : John R. Steel
Publisher : Cambridge University Press
ISBN 13 : 1108896820
Total Pages : 550 pages
Book Rating : 4.1/5 (88 download)

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Book Synopsis A Comparison Process for Mouse Pairs by : John R. Steel

Download or read book A Comparison Process for Mouse Pairs written by John R. Steel and published by Cambridge University Press. This book was released on 2022-11-24 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proves some important new theorems in the theory of canonical inner models for large cardinal hypotheses, a topic of central importance in modern set theory. In particular, the author 'completes' the theory of Fine Structure and Iteration Trees (FSIT) by proving a comparison theorem for mouse pairs parallel to the FSIT comparison theorem for pure extender mice, and then using the underlying comparison process to develop a fine structure theory for strategy mice. Great effort has been taken to make the book accessible to non-experts so that it may also serve as an introduction to the higher reaches of inner model theory. It contains a good deal of background material, some of it unpublished folklore, and includes many references to the literature to guide further reading. An introductory essay serves to place the new results in their broader context. This is a landmark work in inner model theory that should be in every set theorist's library.

Logic Colloquium '02: Lecture Notes in Logic 27

Author : Zoe Chatzidakis
Publisher : CRC Press
ISBN 13 : 1439865906
Total Pages : 370 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Logic Colloquium '02: Lecture Notes in Logic 27 by : Zoe Chatzidakis

Download or read book Logic Colloquium '02: Lecture Notes in Logic 27 written by Zoe Chatzidakis and published by CRC Press. This book was released on 2006-07-13 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: Logic Colloquium '02 includes articles from some of the world's preeminent logicians. The topics span all areas of mathematical logic, but with an emphasis on Computability Theory and Proof Theory. This book will be of interest to graduate students and researchers in the field of mathematical logic.

Logic Colloquium '98

Author : Samuel R. Buss
Publisher : Cambridge University Press
ISBN 13 : 1108618480
Total Pages : 559 pages
Book Rating : 4.1/5 (86 download)

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Book Synopsis Logic Colloquium '98 by : Samuel R. Buss

Download or read book Logic Colloquium '98 written by Samuel R. Buss and published by Cambridge University Press. This book was released on 2017-03-30 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. This volume, the thirteenth publication in the Lecture Notes in Logic series, collects the proceedings of the European Summer Meeting of the Association for Symbolic Logic held at the University of Economics in Prague, August 9–15, 1988. It includes surveys and research from preeminent logicians. The papers in this volume range over all areas of mathematical logic, including proof theory, set theory, model theory, computability theory and philosophy. This book will be of interest to all students and researchers in mathematical logic.

Inner Models and Large Cardinals

Author : Martin Zeman
Publisher : Walter de Gruyter
ISBN 13 : 3110857812
Total Pages : 385 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Inner Models and Large Cardinals by : Martin Zeman

Download or read book Inner Models and Large Cardinals written by Martin Zeman and published by Walter de Gruyter. This book was released on 2011-09-06 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an introduction to inner model theory, an area of set theory which is concerned with fine structural inner models reflecting large cardinal properties of the set theoretic universe. The monograph contains a detailed presentation of general fine structure theory as well as a modern approach to the construction of small core models, namely those models containing at most one strong cardinal, together with some of their applications. The final part of the book is devoted to a new approach encompassing large inner models which admit many Woodin cardinals. The exposition is self-contained and does not assume any special prerequisities, which should make the text comprehensible not only to specialists but also to advanced students in Mathematical Logic and Set Theory.

Ordinal Definability and Recursion Theory: Volume 3

Author : Alexander S. Kechris
Publisher : Cambridge University Press
ISBN 13 : 1316586286
Total Pages : 552 pages
Book Rating : 4.3/5 (165 download)

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Book Synopsis Ordinal Definability and Recursion Theory: Volume 3 by : Alexander S. Kechris

Download or read book Ordinal Definability and Recursion Theory: Volume 3 written by Alexander S. Kechris and published by Cambridge University Press. This book was released on 2016-01-11 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: The proceedings of the Los Angeles Caltech-UCLA 'Cabal Seminar' were originally published in the 1970s and 1980s. Ordinal Definability and Recursion Theory is the third in a series of four books collecting the seminal papers from the original volumes together with extensive unpublished material, new papers on related topics and discussion of research developments since the publication of the original volumes. Focusing on the subjects of 'HOD and its Local Versions' (Part V) and 'Recursion Theory' (Part VI), each of the two sections is preceded by an introductory survey putting the papers into present context. These four volumes will be a necessary part of the book collection of every set theorist.

Set Theory

Author : Carlos A. di Prisco
Publisher : Springer Science & Business Media
ISBN 13 : 9401589887
Total Pages : 229 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Set Theory by : Carlos A. di Prisco

Download or read book Set Theory written by Carlos A. di Prisco and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past 25 years, set theory has developed in several interesting directions. The most outstanding results cover the application of sophisticated techniques to problems in analysis, topology, infinitary combinatorics and other areas of mathematics. This book contains a selection of contributions, some of which are expository in nature, embracing various aspects of the latest developments. Amongst topics treated are forcing axioms and their applications, combinatorial principles used to construct models, and a variety of other set theoretical tools including inner models, partitions and trees. Audience: This book will be of interest to graduate students and researchers in foundational problems of mathematics.

Trends in Set Theory

Author : Samuel Coskey
Publisher : American Mathematical Soc.
ISBN 13 : 1470443325
Total Pages : 207 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Trends in Set Theory by : Samuel Coskey

Download or read book Trends in Set Theory written by Samuel Coskey and published by American Mathematical Soc.. This book was released on 2020-06-18 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of Simon Fest, held in honor of Simon Thomas's 60th birthday, from September 15–17, 2017, at Rutgers University, Piscataway, New Jersey. The topics covered showcase recent advances from a variety of main areas of set theory, including descriptive set theory, forcing, and inner model theory, in addition to several applications of set theory, including ergodic theory, combinatorics, and model theory.

Hod Mice and the Mouse Set Conjecture

Author : Grigor Sargsyan
Publisher : American Mathematical Soc.
ISBN 13 : 1470416921
Total Pages : 186 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hod Mice and the Mouse Set Conjecture by : Grigor Sargsyan

Download or read book Hod Mice and the Mouse Set Conjecture written by Grigor Sargsyan and published by American Mathematical Soc.. This book was released on 2015-06-26 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author develops the theory of Hod mice below ADR+ "Θ is regular". He uses this theory to show that HOD of the minimal model of ADR+ "Θ is regular" satisfies GCH. Moreover, he shows that the Mouse Set Conjecture is true in the minimal model of ADR+ "Θ is regular".

Computational Prospects of Infinity - Part I

Author : Chi-Tat Chong
Publisher : World Scientific
ISBN 13 : 9812794050
Total Pages : 264 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Computational Prospects of Infinity - Part I by : Chi-Tat Chong

Download or read book Computational Prospects of Infinity - Part I written by Chi-Tat Chong and published by World Scientific. This book was released on 2008 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the written versions of the tutorial lectures given at the Workshop on Computational Prospects of Infinity, held from 18 June to 15 August 2005 at the Institute for Mathematical Sciences, National University of Singapore. It consists of articles by four of the leading experts in recursion theory (computability theory) and set theory. The survey paper of Rod Downey provides a comprehensive introduction to algorithmic randomness, one of the most active areas of current research in recursion theory. Theodore A Slaman's article is the first printed account of the ground-breaking work of Slaman-Woodin and Slaman-Shore on the definability of the Turing jump. John Steel presents some results on the properties of derived models of mice, and on the existence of mice with large derived models. The study was motivated by some of the well-known Holy Grails in inner model theory, including the Mouse Set Conjecture. In his presentation, W Hugh Woodin gives an outline of an expanded version (unpublished) on suitable extender sequences, a subject that was developed in the attempt to understand inner model theory for large cardinals beyond the level of superstrong cardinals. The volume serves as a useful guide for graduate students and researchers in recursion theory and set theory to some of the most important and significant developments in these subjects in recent years.

Computational Prospects Of Infinity - Part I: Tutorials

Author : Chi Tat Chong
Publisher : World Scientific
ISBN 13 : 9814471593
Total Pages : 264 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Computational Prospects Of Infinity - Part I: Tutorials by : Chi Tat Chong

Download or read book Computational Prospects Of Infinity - Part I: Tutorials written by Chi Tat Chong and published by World Scientific. This book was released on 2008-05-02 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the written versions of the tutorial lectures given at the Workshop on Computational Prospects of Infinity, held from 18 June to 15 August 2005 at the Institute for Mathematical Sciences, National University of Singapore. It consists of articles by four of the leading experts in recursion theory (computability theory) and set theory. The survey paper of Rod Downey provides a comprehensive introduction to algorithmic randomness, one of the most active areas of current research in recursion theory. Theodore A Slaman's article is the first printed account of the ground-breaking work of Slaman-Woodin and Slaman-Shore on the definability of the Turing jump. John Steel presents some results on the properties of derived models of mice, and on the existence of mice with large derived models. The study was motivated by some of the well-known Holy Grails in inner model theory, including the Mouse Set Conjecture. In his presentation, W Hugh Woodin gives an outline of an expanded version (unpublished) on suitable extender sequences, a subject that was developed in the attempt to understand inner model theory for large cardinals beyond the level of superstrong cardinals.The volume serves as a useful guide for graduate students and researchers in recursion theory and set theory to some of the most important and significant developments in these subjects in recent years.