Set theory for the working mathematician:
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Bibliographische Detailangaben
1. Verfasser: Ciesielski, Krzysztof 1957- (VerfasserIn)
Format: Elektronisch E-Book
Sprache:English
Veröffentlicht: Cambridge Cambridge University Press c1997
Schriftenreihe:London Mathematical Society student texts 39
Schlagworte:
Online-Zugang:FAW01
FAW02
Volltext
Beschreibung:Includes bibliographical references (p. 225-227) and index
Basics of set theory -- - Axiomatic set theory -- - Why axiomatic set theory? -- - The 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 -- - The 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.
Beschreibung:1 Online-Ressource (xi, 236 p.)
ISBN:0521594413
0521594650
1107089069
1139173138
9780521594417
9780521594653
9781107089068
9781139173131

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