Combinatorial Set Theory

2017-12-20 Mathematics

Author : Lorenz J. Halbeisen
Release : 2017-12-20
Genre : Mathematics
Kind : eBook
Book Rating : 314/5 ( reviews)

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Book Synopsis Combinatorial Set Theory by : Lorenz J. Halbeisen

Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen. This book was released on 2017-12-20. Available in PDF, EPUB and Kindle. Book excerpt: 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 of C*-algebras

2019-12-24 Mathematics

Author : Ilijas Farah
Release : 2019-12-24
Genre : Mathematics
Kind : eBook
Book Rating : 939/5 ( reviews)

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Book Synopsis Combinatorial Set Theory of C*-algebras by : Ilijas Farah

Download or read book Combinatorial Set Theory of C*-algebras written by Ilijas Farah. This book was released on 2019-12-24. Available in PDF, EPUB and Kindle. Book excerpt: 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 Set Theory

2011-11-24 Mathematics

Author : Lorenz J. Halbeisen
Release : 2011-11-24
Genre : Mathematics
Kind : eBook
Book Rating : 732/5 ( reviews)

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Book Synopsis Combinatorial Set Theory by : Lorenz J. Halbeisen

Download or read book Combinatorial Set Theory written by Lorenz J. Halbeisen. This book was released on 2011-11-24. Available in PDF, EPUB and Kindle. Book excerpt: 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: Partition Relations for Cardinals

2011-08-18 Mathematics

Author : P. Erdös
Release : 2011-08-18
Genre : Mathematics
Kind : eBook
Book Rating : 457/5 ( reviews)

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Book Synopsis Combinatorial Set Theory: Partition Relations for Cardinals by : P. Erdös

Download or read book Combinatorial Set Theory: Partition Relations for Cardinals written by P. Erdös. This book was released on 2011-08-18. Available in PDF, EPUB and Kindle. Book excerpt: 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

2000-04-01 Computers

Author : Lev D. Beklemishev
Release : 2000-04-01
Genre : Computers
Kind : eBook
Book Rating : 995/5 ( reviews)

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Book Synopsis Combinatorial Set Theory by : Lev D. Beklemishev

Download or read book Combinatorial Set Theory written by Lev D. Beklemishev. This book was released on 2000-04-01. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorial Set Theory

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