000			04166nam a22004933i 4500
001			EBC3114459
003			MiAaPQ
005			20240729124608.0
006			m o d |
007			cr cnu||||||||
008			240724s2003 xx o ||||0 eng d
020			_a9781470403911 _q(electronic bk.)
020			_z9780821834503
035			_a(MiAaPQ)EBC3114459
035			_a(Au-PeEL)EBL3114459
035			_a(CaPaEBR)ebr11041237
035			_a(OCoLC)922965130
040			_aMiAaPQ _beng _erda _epn _cMiAaPQ _dMiAaPQ
050		4	_aQA248 -- .Z37 2004eb
082	0		_a510 s;511.3/22
100	1		_aZapletal, Jindřich.
245	1	0	_aDescriptive Set Theory and Definable Forcing.
250			_a1st ed.
264		1	_aProvidence : _bAmerican Mathematical Society, _c2003.
264		4	_c©2004.
300			_a1 online resource (158 pages)
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
490	1		_aMemoirs of the American Mathematical Society ; _vv.167
505	0		_aIntro -- Contents -- 1 Introduction -- 1.1 The subject of the book -- 1.2 The structure of the book -- 1.3 History and acknowledgments -- 1.4 Notation and literature -- 2 Definable forcing adding a single real -- 2.1 The factor algebras -- 2.2 Basic descriptive set theoretic considerations -- 2.3 Examples -- 2.3.1 The ideal of countable sets -- 2.3.2 The ideal of σ bounded sets -- 2.3.3 The ideal of meager sets -- 2.3.4 The cmin ideal -- 2.3.5 Ideals generated by closed sets -- 2.3.6 The Laver ideal -- 2.3.7 Ideals associated with creature forcings -- 2.3.8 The Lebesgue null ideal -- 2.3.9 Mathias forcing -- 2.3.10 The E[sub(0)] ideal -- 2.3.11 Silver forcing -- 2.3.12 The σ porous ideal -- 2.3.13 Steprans forcing -- 2.3.14 Hausdorff measures -- 2.3.15 Unions of ideals -- 2.3.16 Cross-products of ideals -- 2.3.17 The σ splitting ideal -- 2.3.18 Namba forcing -- 3 The countable support iteration -- 3.1 A topological view of the iteration -- 3.2 The iterated Fubini powers of an ideal -- 3.3 A dichotomy for Π[sup(1)][sub(1)]on Σ[sup(1)][sub(1)] ideals -- 3.4 A dichotomy for almost full ideals -- 3.5 Other dichotomies -- 3.6 Cardinal invariants of the iterated ideals -- 4 Other forcings -- 4.1 Illfounded iterations -- 4.1.1 Strongly proper forcings -- 4.1.2 The ideals associated with countable length iterations -- 4.1.3 The properties of the factor ordering -- 4.1.4 The uncountable length -- 4.1.5 Sacks forcing iteration -- 4.2 Towers of ideals -- 4.2.1 Shooting a club with no infinite subset in the ground model -- 4.2.2 Shooting a club with finite intersection with every ground model ordertype w set -- 5 Applications -- 5.1 Ciesielski-Pawlikowski Axiom CPA and variations -- 5.1.1 The axioms -- 5.1.2 Absoluteness with no large cardinals -- 5.1.3 Absoluteness with large cardinals -- 5.2 Duality theorems -- 5.3 Interpolation theorems.
505	8		_a5.4 Preservation theorems -- 5.4.1 Ergodic ideals -- 5.4.2 Preservation and ergodicity -- 5.4.3 Uniformity of σ ideal generated by closed sets -- A: Examples of cardinal invariants -- B: The syntax of cardinal invariants -- B.1 The covering numbers -- B.2 The tame and very tame invariants -- C: Effective descriptive set theory -- D: Large cardinals -- D.1 The absoluteness results -- D.2 The determinacy results.
588			_aDescription based on publisher supplied metadata and other sources.
590			_aElectronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650		0	_aDescriptive set theory.
650		0	_aForcing (Model theory).
650		0	_aContinuum hypothesis.
650		0	_aBorel sets.
655		4	_aElectronic books.
776	0	8	_iPrint version: _aZapletal, Jindřich _tDescriptive Set Theory and Definable Forcing _dProvidence : American Mathematical Society,c2003 _z9780821834503
797	2		_aProQuest (Firm)
830		0	_aMemoirs of the American Mathematical Society
856	4	0	_uhttps://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114459 _zClick to View
999			_c69954 _d69954