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ℙ max variations related to slaloms
Author(s) -
Yorioka Teruyuki
Publication year - 2006
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.200510028
Subject(s) - absoluteness , mathematics , cofinality , ideal (ethics)
We prove the iteration lemmata, which are the key lemmata to show that extensions by Pmax variations satisfy absoluteness for Π 2 ‐statements in the structure 〈 H ( ω 2 ), ∈, NS ω 1 , R 〉 for some set R of reals in L (ℝ), for the following statements: (1) The cofinality of the null ideal is ℵ 1 . (2) There exists a good basis of the strong measure zero ideal. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)