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On the weak Freese–Nation property of ?(ω)

✍ Scribed by Sakaé Fuchino; Stefan Geschke; Lajos Soukupe

Publisher
Springer
Year
2001
Tongue
English
Weight
101 KB
Volume
40
Category
Article
ISSN
0933-5846

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On the weak Freese-Nation property of co
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The following results are proved: (a) In a model obtained by adding ℵ2 Cohen reals, there is always a c.c.c. complete Boolean algebra without the weak Freese-Nation property. (b) Modulo the consistency strength of a supercompact cardinal, the existence of a c.c.c. complete Boolean algebra without t

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## Abstract 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 versio