Combinatorial Set Theory
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Combinatorial Set Theory
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Author : Lorenz J. Halbeisen
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-24
Combinatorial Set Theory written by Lorenz J. Halbeisen 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 2011-11-24 with Mathematics categories.
This book provides a self-contained introduction to modern set theory and also opens up some more advanced areas of current research in this field. The first part offers an overview of classical set theory wherein the focus lies on the axiom of choice and Ramsey theory. In the second part, the sophisticated technique of forcing, originally developed by Paul Cohen, is explained in great detail. With this technique, one can show that certain statements, like the continuum hypothesis, are neither provable nor disprovable from the axioms of set theory. In the last part, some topics of classical set theory are revisited and further developed in the light of forcing. The notes at the end of each chapter put the results in a historical context, and the numerous related results and the extensive list of references lead the reader to the frontier of research. This book will appeal to all mathematicians interested in the foundations of mathematics, but will be of particular use to graduates in this field.
Combinatorial Set Theory
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Author : Lorenz J. Halbeisen
language : en
Publisher: Springer
Release Date : 2017-12-20
Combinatorial Set Theory written by Lorenz J. Halbeisen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-20 with Mathematics categories.
This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. 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 and historical remarks at the end of each chapter, this book is suitable for self-study.
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.
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.
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 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.
Combinatorial Group Theory
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Author : Roger C. Lyndon
language : en
Publisher: Springer
Release Date : 2015-03-12
Combinatorial Group Theory written by Roger C. Lyndon and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-12 with Mathematics categories.
From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews
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 : Simon Thomas
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Set Theory written by Simon Thomas and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Set theory categories.
This volume presents the proceedings from the Mid-Atlantic Mathematical Logic Seminar (MAMLS) conference held in honor of Andras Hajnal at the DIMACS Center, Rutgers University (New Brunswick, NJ). Articles include both surveys and high-level research papers written by internationally recognized experts in the field of set theory. Many of the current active areas of set theory are represented in this volume. It includes research papers on combinatorial set theory, set theoretictopology, descriptive set theory, and set theoretic algebra. There are valuable surveys on combinatorial set theory, fragments of the proper forcing axiom, and the reflection properties of stationary sets. The book also includes an exposition of the ergodic theory of lattices in higher rank semisimpleLie groups-essential reading for anyone who wishes to understand much of the recent work on countable Borel equivalence relations.
The History Of Combinatorial Group Theory
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Author : B. Chandler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The History Of Combinatorial Group Theory written by B. Chandler 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.
One of the pervasive phenomena in the history of science is the development of independent disciplines from the solution or attempted solutions of problems in other areas of science. In the Twentieth Century, the creation of specialties witqin the sciences has accelerated to the point where a large number of scientists in any major branch of science cannot understand the work of a colleague in another subdiscipline of his own science. Despite this fragmentation, the development of techniques or solutions of problems in one area very often contribute fundamentally to solutions of problems in a seemingly unrelated field. Therefore, an examination of this phenomenon of the formation of independent disciplines within the sciences would contrib ute to the understanding of their evolution in modern times. We believe that in this context the history of combinatorial group theory in the late Nineteenth Century and the Twentieth Century can be used effectively as a case study. It is a reasonably well-defined independent specialty, and yet it is closely related to other mathematical disciplines. The fact that combinatorial group theory has, so far, not been influenced by the practical needs of science and technology makes it possible for us to use combinatorial group theory to exhibit the role of the intellectual aspects of the development of mathematics in a clearcut manner. There are other features of combinatorial group theory which appear to make it a reasona ble choice as the object of a historical study.