Set Theory for the Working Mathematician
Krzysztof. Ciesielski
Bok Engelsk 1997 · Electronic books.
| Annen tittel | |
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| Utgitt | Cambridge : Cambridge University Press , c1997
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| Omfang | 1 online resource (254 p.)
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| Opplysninger | Description based upon print version of record.. - Cover; Series Page; Title; Copyright; Dedication; Contents; Preface; Part I: Basics of set theory; Chapter 1 Axiomatic set theory; 1.1 Why axiomatic set theory?; 1.2 The language and the basic axioms; EXERCISES; Chapter 2 Relations, functions, and Cartesian product; 2.1 Relations and the axiom of choice; EXERCISES; 2.2 Functions and the replacement scheme axiom; EXERCISES; 2.3 Generalized union, intersection, and Cartesian product; EXERCISES; 2.4 Partial- and linear-order relations; EXERCISES; Chapter 3 Natural numbers, integers, and real numbers; 3.1 Natural numbers; EXERCISES. - 3.2 Integers and rational numbersEXERCISES; 3.3 Real numbers; EXERCISES; Part II: Fundamental tools of set theory; Chapter 4 Well orderings and transfinite induction; 4.1 Well-ordered sets and the axiom of foundation; EXERCISES; 4.2 Ordinal numbers; EXERCISES; 4.3 Definitions by transfinite induction; EXERCISES; 4.4 Zorn's lemma in algebra, analysis, and topology; EXERCISES; Chapter 5 Cardinal numbers; 5.1 Cardinal numbers and the continuum hypothesis; EXERCISES; 5.2 Cardinal arithmetic; EXERCISES; 5.3 Cofinality; EXERCISES; Part III: The power of recursive definitions. - 8.3 Suslin hypothesis and diamond principleEXERCISES; Chapter 9 Forcing; 9.1 Elements of logic and other forcing preliminaries; EXERCISES; 9.2 Forcing method and a model for ¬CH; EXERCISES; 9.3 Model for CH and ◊; EXERCISES; 9.4 Product lemma and Cohen model; EXERCISES; 9.5 Model for MA+¬CH; EXERCISES; Appendix A Axioms of set theory; Appendix B Comments on the forcing method; Appendix C Notation; References; Index. - Chapter 6 Subsets of Rn6.1 Strange subsets of IRn and the diagonalization argument; EXERCISES; 6.2 Closed sets and Borel sets; EXERCISES; 6.3 Lebesgue-measurable sets and sets with the Baire property; EXERCISES; Chapter 7 Strange real functions; 7.1 Measurable and nonmeasurable functions; EXERCISES; 7.2 Darboux functions; EXERCISES; 7.3 Additive functions and Hamel bases; EXERCISES; 7.4 Symmetrically discontinuous functions; EXERCISES; Part IV: When induction is too short; Chapter 8 Martin's axiom; 8.1 Rasiowa-Sikorski lemma; EXERCISES; 8.2 Martin's axiom; EXERCISES. - Presents those methods of modern set theory most applicable to other areas of pure mathematics.
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| Emner | |
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| Dewey | |
| ISBN | 0521594413. - 0521594650
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