Combinatorial Set Theory

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Combinatorial Set Theory Partition Relations For Cardinals

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Author : P. Erdös
language : en
Publisher: Elsevier
Release Date : 2011-08-18

Combinatorial Set Theory Partition Relations For Cardinals written by P. Erdös and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.

This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel'skii's famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of recent inequalities for cardinal powers that were obtained in the wake of Silver's breakthrough result saying that the continuum hypothesis can not first fail at a singular cardinal of uncountable cofinality.

Combinatorial Set Theory

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Author : Lorenz J. Halbeisen
language : en
Publisher:
Release Date : 2017

Combinatorial Set Theory written by Lorenz J. Halbeisen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with Combinatorial analysis categories.

Combinatorial Set Theory

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Author : Lev D. Beklemishev
language : en
Publisher: Elsevier
Release Date : 2000-04-01

Combinatorial Set Theory written by Lev D. Beklemishev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Computers categories.

Combinatorial Set Theory

Combinatorial Set Theory

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Author : Lorenz Halbeisen
language : en
Publisher:
Release Date : 2025

Combinatorial Set Theory written by Lorenz Halbeisen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025 with Discrete mathematics categories.

Part I: Preliminary -- 1 The Setting -- 2 First-Order Logic in a Nutshell -- 3 Axioms of Set Theory -- Part II: Topics in Combinatorial Set Theory -- 4 Overture: Ramsey's Theorem -- 5 Cardinal Relations in ZF Only -- 6 Forms of Choice -- 7 How to Make Two Balls from One -- 8 Models of Set Theory with Atoms -- 9 Thirteen Cardinals and Their Relations -- 10 The Shattering Number Revisited -- 11 Happy Families and Their Relatives -- 12 Coda: A Dual Form of Ramsey's Theorem -- Part III: From Martin's Axiom to Cohen's Forcing -- 13 The Idea of Forcing -- 14 Martin's Axiom -- 15 The Notion of Forcing -- 16 Proving Unprovability -- 17 Models in Which AC Fails -- 18 Combining Forcing Notions -- 19 Models in Which p=c -- 20 Suslin's Problem -- Part IV: Combinatorics of Forcing Extensions -- 21 Properties of Forcing Extensions -- 22 Cohen Forcing Revisited -- 23 Sacks Forcing -- 24 Silver-Like Forcing Notions -- 25 Miller Forcing -- 26 Mathias Forcing -- 27 Laver Forcing -- 28 How Many Ramsey Ultrafilters Exist? -- 29 Suite.

Combinatorial Set Theory

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Author : Lorenz J. Halbeisen
language : en
Publisher: Springer Nature
Release Date : 2025-05-26

Combinatorial Set Theory written by Lorenz J. Halbeisen and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-26 with Mathematics categories.

This book, now in a revised and extended third edition, provides a comprehensive and accessible introduction to modern axiomatic set theory. After an overview of basic notions in combinatorics and first-order logic, and discussing in great detail the axioms of set theory, the author outlines in the second part the main topics of classical set theory, including Ramsey theory and the axiom of choice. As an application of the axiom of choice, a complete proof of Robinson's construction for doubling a ball by dividing it into only five parts is given. For the new edition, the chapter on permutation models has been extended, and recent results in set theory without the axiom of choice and about cardinal characteristics have been added. The third part explains the sophisticated technique of forcing from scratch, now including more details about iterated forcing. The technique is then used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In particular, it is shown that both Martin's Axiom and Suslin's Hypothesis are independent of the axioms of set theory. The final part, with a new chapter on Laver forcing, is mainly concerned with consistency results obtained by iterations of forcing notions such as Cohen forcing, Sacks forcing, and Mathias forcing. The part begins with an extended chapter on countable support iterations of proper forcing notions, now also including proofs of some preservation theorems such as preservation of properness and of certain ultrafilters. In the following chapters, various consistency results concerning possible relations between cardinal characteristics and the existence of Ramsey ultrafilters are presented. For example, a detailed proof of Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters is given. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists, historical remarks, and related results at the end of the chapters, this book is also suitable for self-study.

Combinatorial Set Theory Of C Algebras

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Author : Ilijas Farah
language : en
Publisher: Springer Nature
Release Date : 2019-12-24

Combinatorial Set Theory Of C Algebras written by Ilijas Farah and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-24 with Mathematics categories.

This book explores and highlights the fertile interaction between logic and operator algebras, which in recent years has led to the resolution of several long-standing open problems on C*-algebras. The interplay between logic and operator algebras (C*-algebras, in particular) is relatively young and the author is at the forefront of this interaction. The deep level of scholarship contained in these pages is evident and opens doors to operator algebraists interested in learning about the set-theoretic methods relevant to their field, as well as to set-theorists interested in expanding their view to the non-commutative realm of operator algebras. Enough background is included from both subjects to make the book a convenient, self-contained source for students. A fair number of the exercises form an integral part of the text. They are chosen to widen and deepen the material from the corresponding chapters. Some other exercises serve as a warmup for the latter chapters.

Set Theory

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Author : A. Hajnal
language : en
Publisher:
Release Date : 2014-05-14

Set Theory written by A. Hajnal and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with MATHEMATICS categories.

This is a classic introduction to set theory, from the basics through to the modern tools of combinatorial set theory.

Combinatorial Group Theory

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Author : Wilhelm Magnus
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01

Combinatorial Group Theory written by Wilhelm Magnus and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.

This seminal, much-cited account begins with a fairly elementary exposition of basic concepts and a discussion of factor groups and subgroups. The topics of Nielsen transformations, free and amalgamated products, and commutator calculus receive detailed treatment. The concluding chapter surveys word, conjugacy, and related problems; adjunction and embedding problems; and more. Second, revised 1976 edition.

Finite And Infinite Combinatorics In Sets And Logic

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Author : Norbert W Sauer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Finite And Infinite Combinatorics In Sets And Logic written by Norbert W Sauer 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 2012-12-06 with Mathematics categories.

This volume contains the accounts of papers delivered at the Nato Advanced Study Institute on Finite and Infinite Combinatorics in Sets and Logic held at the Banff Centre, Alberta, Canada from April 21 to May 4, 1991. As the title suggests the meeting brought together workers interested in the interplay between finite and infinite combinatorics, set theory, graph theory and logic. It used to be that infinite set theory, finite combinatorics and logic could be viewed as quite separate and independent subjects. But more and more those disciplines grow together and become interdependent of each other with ever more problems and results appearing which concern all of those disciplines. I appreciate the financial support which was provided by the N. A. T. O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the Department of Mathematics and Statistics of the University of Calgary. 11l'te meeting on Finite and Infinite Combinatorics in Sets and Logic followed two other meetings on discrete mathematics held in Banff, the Symposium on Ordered Sets in 1981 and the Symposium on Graphs and Order in 1984. The growing inter-relation between the different areas in discrete mathematics is maybe best illustrated by the fact that many of the participants who were present at the previous meetings also attended this meeting on Finite and Infinite Combinatorics in Sets and Logic.

Set Theory

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Author : Andras Hajnal
language : en
Publisher: Cambridge University Press
Release Date : 1999-11-11

Set Theory written by Andras Hajnal and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-11-11 with Mathematics categories.

This is a classic introduction to set theory in three parts. The first part gives a general introduction to set theory, suitable for undergraduates; complete proofs are given and no background in logic is required. Exercises are included, and the more difficult ones are supplied with hints. An appendix to the first part gives a more formal foundation to axiomatic set theory, supplementing the intuitive introduction given in the first part. The final part gives an introduction to modern tools of combinatorial set theory. This part contains enough material for a graduate course of one or two semesters. The subjects discussed include stationary sets, delta systems, partition relations, set mappings, measurable and real-valued measurable cardinals. Two sections give an introduction to modern results on exponentiation of singular cardinals, and certain deeper aspects of the topics are developed in advanced problems.