Set theory for the working mathematician
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
c1997
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| Schriftenreihe: | London Mathematical Society student texts
39 |
| Schlagworte: | |
| Online-Zugang: | DE-1046 DE-1047 Volltext |
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| 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. |
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| Beschreibung: | 1 Online-Ressource (xi, 236 p.) |
| ISBN: | 0521594413 0521594650 1107089069 1139173138 9780521594417 9780521594653 9781107089068 9781139173131 |