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Author Ciesielski, Krzysztof, 1957-

Title Set theory for the working mathematician / Krzysztof Ciesielski.

Publication Info. Cambridge ; New York : Cambridge University Press, [1997]
©1997

Item Status

Description 1 online resource (xi, 236 pages).
Physical Medium polychrome
Description text file
Series London Mathematical Society student texts ; 39
London Mathematical Society student texts ; 39.
Bibliography Includes bibliographical references (pages 225-227) and index.
Contents Basics of set theory -- Axiomatic set theory -- Why axiomatic set theory? -- Language and the basic axioms -- Relations, functions, and Cartesian product -- Relations and the axiom of choice -- Functions and the replacement scheme axiom -- Generalized union, intersection, and Cartesian product -- Partial- and linear-order relations -- Natural numbers, integers, and real numbers -- Natural numbers -- Integers and rational numbers -- Real numbers -- Fundamental tools of set theory -- Well orderings and transfinite induction -- Well-ordered sets and the axiom of foundation -- Ordinal numbers -- Definitions by transfinite induction -- Zorn's lemma in algebra, analysis, and topology -- Cardinal numbers -- Cardinal numbers and the continuum hypothesis -- Cardinal arithmetic -- Cofinality -- Power of recursive definitions -- Subsets of R[superscript n] -- Strange subsets of R[superscript n] and the diagonalization argument -- Closed sets and Borel sets -- Lebesgue-measurable sets and sets with the Baire property -- Strange real functions -- Measurable and nonmeasurable functions -- Darboux functions -- Additive functions and Hamel bases -- Symmetrically discontinuous functions -- When induction is too short -- Martin's axiom -- Rasiowa-Sikorski lemma -- Martin's axiom -- Suslin hypothesis and diamond principle -- Forcing -- Elements of logic and other forcing preliminaries -- Forcing method and a model for [not sign]CH -- Model for CH and [diamonds suit symbol] -- Product lemma and Cohen model -- Model for MA+[not sign]CH.
Local Note eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject Set theory.
Set theory.
Genre/Form Electronic books.
Other Form: Print version: Ciesielski, Krzysztof, 1957- Set theory for the working mathematician. Cambridge ; New York : Cambridge University Press, ©1997 0521594413 (DLC) 97010533 (OCoLC)36621835
ISBN 9781139173131 (electronic book)
1139173138 (electronic book)
9781107089068 (electronic book)
1107089069 (electronic book)
0521594413
9780521594417
0521594650
9780521594653