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Problems and Theorems in Classical Set Theory (Problem Books in Mathematics)

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Problems and Theorems in Classical Set Theory (Problem Books in Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

This volume contains a variety of problems from classical set theory and represents the first comprehensive collection of such problems. Many of these problems are also related to other fields of mathematics, including algebra, combinatorics, topology and real analysis. Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way that earlier problems help in the solution of later ones. For many of the problems, the authors also trace the history of the problems and then provide proper reference at the end of the solution.

Synopsis:

This is the first comprehensive collection of problems in set theory. It contains well chosen sequences of exercises. Most of the problems are challenging and require work, wit, and inspiration. The book is destined to become a classic.

Table of Contents

Foreword.- Problems: Operations on sets.- Countability.- Equivalence.- Continuum.- Sets of reals and real functions.- Ordered sets.- Order types.- Ordinals.- Ordinal arithmetic.- Cardinals.- Partially ordered sets.- Transfinite enumeration.- Euclidean spaces.- Zorn's lemma.- Hamel bases.- The continuum hypothesis.- Ultrafilters on w.- Families of sets.- The Banach-Tarski paradox.- Stationary sets in w1.- Stationary sets in larger cardinals.- Canonical functions.- Infinite graphs.- Partition relations.- \triangle systems.- Set mappings.- Trees.- The measure problem.- Stationary sets.- The axiom of choice.- Well founded sets and the axiom of foundation.- Solutions: Operations on sets.- Countability.- Equivalence.- Continuum.- Sets of reals and real functions.- Ordered sets.- Order types.- Ordinals.- Ordinal arithmetic.- Cardinals.- Partially ordered sets.- Transfinite enumeration.- Euclidean spaces.- Zorn's lemma.- Hamel bases.- The continuum hypothesis.- Ultrafilters on w Families of sets The Banach-Tarski paradox Stationary sets in w1.- Stationary sets in larger cardinals.- Canonical functions.- Infinite graphs.- Partition relations.- \triangle-systems.- Set mappings.- Trees.- The measure problem.- Stationary sets.- The axiom of choice Well founded sets and the axiom of foundation.- Appendix.- Glossary of Concepts.- Glossary of Symbols.- Index.

Product Details

ISBN:
9781441921406
Author:
Komjath, Peter
Publisher:
Springer
Author:
Totik, Vilmos
Subject:
Logic
Subject:
Mathematical Logic and Foundations
Subject:
Combinatorics
Subject:
Combinatorics <P>This is the first comprehensive collection of problems in set theory. But rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. They vary in difficulty, and are organized in such a way th
Subject:
Mathematics-Logic and Philosophy
Subject:
Mathematics : Set Theory
Copyright:
Edition Description:
Softcover reprint of hardcover 1st ed. 2006
Series:
Problem Books in Mathematics
Publication Date:
20101124
Binding:
TRADE PAPER
Language:
English
Pages:
528
Dimensions:
235 x 155 mm 791 gr

Related Subjects


Science and Mathematics » Mathematics » Advanced
Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » Foundations and Logic
Science and Mathematics » Mathematics » Logic and Philosophy
Science and Mathematics » Mathematics » Set Theory

Problems and Theorems in Classical Set Theory (Problem Books in Mathematics) New Trade Paper
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$64.95 In Stock
Product details 528 pages Springer - English 9781441921406 Reviews:
"Synopsis" by , This is the first comprehensive collection of problems in set theory. It contains well chosen sequences of exercises. Most of the problems are challenging and require work, wit, and inspiration. The book is destined to become a classic.
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