000 02343nam a22003618i 4500
001 CR9780511542732
003 UkCbUP
005 20200124160237.0
006 m|||||o||d||||||||
007 cr||||||||||||
008 090505s2008||||enk o ||1 0|eng|d
020 _a9780511542732 (ebook)
020 _z9780521874267 (hardback)
040 _aUkCbUP
_beng
_erda
_cUkCbUP
050 0 0 _aQA248
_b.Z37 2008
082 0 4 _a511.322
_222
100 1 _aZapletal, Jindřich,
_d1969-
_eauthor.
245 1 0 _aForcing idealized /
_cJindřich Zapletal.
264 1 _aCambridge :
_bCambridge University Press,
_c2008.
300 _a1 online resource (vi, 314 pages) :
_bdigital, PDF file(s).
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
490 1 _aCambridge tracts in mathematics ;
_v174
500 _aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 _aIntroduction -- Basics -- Properties -- Examples -- Operations -- Applications -- Questions.
520 _aDescriptive set theory and definable proper forcing are two areas of set theory that developed quite independently of each other. This monograph unites them and explores the connections between them. Forcing is presented in terms of quotient algebras of various natural sigma-ideals on Polish spaces, and forcing properties in terms of Fubini-style properties or in terms of determined infinite games on Boolean algebras. Many examples of forcing notions appear, some newly isolated from measure theory, dynamical systems, and other fields. The descriptive set theoretic analysis of operations on forcings opens the door to applications of the theory: absoluteness theorems for certain classical forcing extensions, duality theorems, and preservation theorems for the countable support iteration. Containing original research, this text highlights the connections that forcing makes with other areas of mathematics, and is essential reading for academic researchers and graduate students in set theory, abstract analysis and measure theory.
650 0 _aDescriptive set theory.
650 0 _aForcing (Model theory)
776 0 8 _iPrint version:
_z9780521874267
830 0 _aCambridge tracts in mathematics ;
_v174.
856 4 0 _uhttps://doi.org/10.1017/CBO9780511542732
999 _c518149
_d518147