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σ-short Boolean algebras

✍ Scribed by Makoto Takahashi; Yasuo Yoshinobu

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 145 KB
Volume: 49
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200310058

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We introduce properties of Boolean algebras which are closely related to the existence of winning strategies in the Banach‐Mazur Boolean game. A σ‐short Boolean algebra is a Boolean algebra that has a dense subset in which every strictly descending sequence of length ω does not have a nonzero lower bound. We give a characterization of σ‐short Boolean algebras and study properties of σ‐short Boolean algebras. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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