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Understanding preservation theorems, II
Author(s) -
Schlindwein Chaz
Publication year - 2010
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200910109
Subject(s) - forcing (mathematics) , mathematics , countable set , bounding overwatch , property (philosophy) , exposition (narrative) , set (abstract data type) , discrete mathematics , outer measure , computer science , mathematical analysis , artificial intelligence , art , philosophy , literature , epistemology , programming language , fractal dimension , fractal , minkowski–bouligand dimension
We present an exposition of much of Sections VI.3 and XVIII.3 from Shelah's book Proper and Improper Forcing . This covers numerous preservation theorems for countable support iterations of proper forcing, including preservation of the property “no new random reals over V ”, the property “reals of the ground model form a non‐meager set”, the property “every dense open set contains a dense open set of the ground model”, and preservation theorems related to the weak bounding property, the weak ω ω ‐bounding property, and the property “the set of reals of the ground model has positive outer measure” (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)