Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Playful Boolean algebras


Author: Boban Veličković
Journal: Trans. Amer. Math. Soc. 296 (1986), 727-740
MSC: Primary 06E10; Secondary 03E40, 03G05
MathSciNet review: 846604
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We show that for an atomless complete Boolean algebra $ \mathcal{B}$ of density $ \leq {2^{{\aleph _0}}}$, the Banach-Mazur, the split and choose, and the Ulam game on $ \mathcal{B}$ are equivalent. Moreover, one of the players has a winning strategy just in trivial cases: Empty wins iff $ \mathcal{B}$ adds a real; Nonempty wins iff $ \mathcal{B}$ has a $ \sigma $-closed dense set. This extends some previous results of Foreman, Jech, and Vojtáš


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 06E10, 03E40, 03G05

Retrieve articles in all journals with MSC: 06E10, 03E40, 03G05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0846604-0
PII: S 0002-9947(1986)0846604-0
Keywords: Boolean algebras, infinite games, trees, measurable cardinals
Article copyright: © Copyright 1986 American Mathematical Society