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A short proof of the preservation of the ω ω ‐bounding property
Author(s) -
Schlindwein Chaz
Publication year - 2004
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.200310072
Subject(s) - lemma (botany) , bounding overwatch , mathematical proof , mathematics , property (philosophy) , discrete mathematics , combinatorics , computer science , ecology , philosophy , geometry , poaceae , epistemology , artificial intelligence , biology
There are two versions of the Proper Iteration Lemma. The stronger (but less well‐known) version can be used to give simpler proofs of iteration theorems (e.g., [7, Lemma 24] versus [9, Theorem IX.4.7]). In this paper we give another demonstration of the fecundity of the stronger version by giving a short proof of Shelah's theorem on the preservation of the ω ω ‐bounding property. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)