000			04198nam a22004455i 4500
001			978-0-387-36219-9
003			DE-He213
005			20250710083956.0
007			cr nn 008mamaa
008			100301s2006 xxu| s |||| 0|eng d
020			_a9780387362199 _a99780387362199
024	7		_a10.1007/0-387-36219-3 _2doi
082	0	4	_a511.3 _223
100	1		_aKomjáth, Péter. _eauthor.
245	1	0	_aProblems and Theorems in Classical Set Theory _h[recurso electrónico] / _cby Péter Komjáth, Vilmos Totik.
264		1	_aNew York, NY : _bSpringer New York, _c2006.
300			_aXII, 516 p. _bonline resource.
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_atext file _bPDF _2rda
490	1		_aProblem Books in Mathematics, _x0941-3502
505	0		_aProblems -- Operations on sets -- Countability -- Equivalence -- Continuum -- Sets of reals and real functions -- Ordered sets -- Order types -- Ordinals -- Ordinal arithmetic -- Cardinals -- Partially ordered sets -- Transfinite enumeration -- Euclidean spaces -- Zorn's lemma -- Hamel bases -- The continuum hypothesis -- Ultrafilters on ? -- Families of sets -- The Banach-Tarski paradox -- Stationary sets in ?1 -- Stationary sets in larger cardinals -- Canonical functions -- Infinite graphs -- Partition relations -- ?-systems -- Set mappings -- Trees -- The measure problem -- Stationary sets in [?]<? -- The axiom of choice -- Well-founded sets and the axiom of foundation -- Solutions -- Operations on sets -- Countability -- Equivalence -- Continuum -- Sets of reals and real functions -- Ordered sets -- Order types -- Ordinals -- Ordinal arithmetic -- Cardinals -- Partially ordered sets -- Transfinite enumeration -- Euclidean spaces -- Zorn's lemma -- Hamel bases -- The continuum hypothesis -- Ultrafilters on ? -- Families of sets -- The Banach-Tarski paradox -- Stationary sets in ?1 -- Stationary sets in larger cardinals -- Canonical functions -- Infinite graphs -- Partition relations -- ?-systems -- Set mappings -- Trees -- The measure problem -- Stationary sets in [?]<? -- The axiom of choice -- Well-founded sets and the axiom of foundation.
520			_aThis is the first comprehensive collection of problems in set theory. Most of classical set theory is covered, classical in the sense that independence methods are not used, but classical also in the sense that most results come from the period between 1920-1970. Many problems are also related to other fields of mathematics such as algebra, combinatorics, topology and real analysis. The authors choose not to concentrate on the axiomatic framework, although some aspects are elaborated (axiom of foundation and the axiom of choice). Rather than using drill exercises, most problems are challenging and require work, wit, and inspiration. The problems are organized in a way that earlier problems help in the solution of later ones. For many problems, the authors trace the origin and provide proper references at the end of the solution. The book follows a tradition of Hungarian mathematics started with Pólya-Szegõ's problem book in analysis and continued with Lovász' problem book in combinatorics. This is destined to become a classic, and will be an important resource for students and researchers. Péter Komjáth is a professor of mathematics at the Eötvös Lóránd University, Budapest. Vilmos Totik is a professor of mathematics at the University of South Florida, Tampa and University of Szeged.
650		0	_aMATHEMATICS.
650		0	_aCOMBINATORICS.
650		0	_aLOGIC, SYMBOLIC AND MATHEMATICAL.
650	1	4	_aMATHEMATICS.
650	2	4	_aMATHEMATICAL LOGIC AND FOUNDATIONS.
650	2	4	_aCOMBINATORICS.
700	1		_aTotik, Vilmos. _eauthor.
710	2		_aSpringerLink (Online service)
773	0		_tSpringer eBooks
776	0	8	_iPrinted edition: _z9780387302935
830		0	_aProblem Books in Mathematics, _x0941-3502
856	4	0	_uhttp://dx.doi.org/10.1007/0-387-36219-3 _zVer el texto completo en las instalaciones del CICY
912			_aZDB-2-SMA
942			_2ddc _cER
999			_c57485 _d57485