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σ ‐short Boolean algebras
Author(s) -
Takahashi Makoto,
Yoshinobu Yasuo
Publication year - 2003
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.200310058
Subject(s) - stone's representation theorem for boolean algebras , complete boolean algebra , boolean algebras canonically defined , free boolean algebra , mathematics , two element boolean algebra , interior algebra , boolean algebra , parity function , boolean expression , discrete mathematics , combinatorics , boolean function , algebra over a field , pure mathematics , jordan algebra , algebra representation
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)