000			02400nam a22002897a 4500
999			_c73316 _d73316
003			CITU
005			20230215092747.0
007			cr an aaaaaaaa
008			210816b ||||| |||| 00| 0 eng d
020			_a9781139173131
041			_aeng.
082			_a511.322
100	1		_aCiesielski, Krzysztof. _d1957- _eauthor
245			_aSet theory for the working mathematician / _cKrzysztof Ciesielski.
264		1	_aCambridge: _bCambridge University Press, _cc2012
300			_a1 online resource (xi, 236 pages) :
336			_2rdacontent _atext _btext
337			_2rdamedia _acomputer _bc
338			_2rdacarrier _aonline resource _bcr
504			_aIncludes bibliographical references (p. 225-227) and index.
505			_aPart I. Basics of Set Theory: 1. Axiomatic set theory 2. Relations, functions and Cartesian product 3. Natural, integer and real numbers Part II. Fundamental Tools of Set Theory: 4. Well orderings and transfinite induction 5. Cardinal numbers Part III. The Power of Recursive Definitions: 6. Subsets of Rn 7. Strange real functions Part IV. When Induction is Too Short: 8. Martin's axiom 9. Forcing Part V. Appendices: A. Axioms of set theory B. Comments on forcing method C. Notation.
520			_aThis text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of "modern" set theory: Martin's Axiom, the Diamond Principle, and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.
650		0	_aSet theory.
655		0	_aElectronic books.
856			_yFull text available at Cambridge University Press Click here to view _uhttps://www.cambridge.org/core/books/set-theory-for-the-working-mathematician/265BF1E67363492A762DF85B136DA8B7
942			_2ddc _cER