On the weak distributivity game
type: Item
instance of: scholarly article
title: On the weak distributivity game
zbMATH Open document ID: 0798.03054
DOI: 10.1016/0168-0072(94)90077-9
author: Anastasis Kamburelis
published in: Annals of Pure and Applied Logic
publication date: 1994-11-03T00:00:00Z
review text: The game \({\mathcal G}_{\text{fin}} (\kappa)\) of \textit{T. J. Jech} [ibid. 26, 11-29 (1984; Zbl 0555.03025)] is studied. The implication: if \({\mathcal B}\) is weakly \((\omega,\kappa)\)-distributive then player I does not have a winning strategy in the game \({\mathcal G}_{\text{fin}} (\kappa)\) is considered. It is shown that the implication is true for a proper complete Boolean algebra [\textit{S. Shelah}, Proper forcing (Lect. Notes Math. 940) (1982; Zbl 0495.03035)], but is not true in general. Also, a weakly \((\omega, \infty)\)-distributive Boolean algebra is obtained such that player I has a winning strategy in the game \({\mathcal G}_ \omega (\omega_ 2)\), solving problems 3 and 4 of the paper of Jech.
Mathematics Subject Classification ID: 03E40
Mathematics Subject Classification ID: 06E10
Mathematics Subject Classification ID: 91A44
Mathematics Subject Classification ID: 91A05
zbMATH DE Number: 513339
zbMATH Keywords: weak distributivity game
zbMATH Keywords: weakly distributive Boolean algebra
zbMATH Keywords: proper complete Boolean algebra
reviewed by: J. Donald Monk
MaRDI profile type: Publication
full work available at URL: 0168-0072(94)90077-9
OpenAlex ID: W2030469676
cites work: Forcing closed unbounded sets
cites work: Saturation Properties of Ideals in Generic Extensions. I
cites work: More game-theoretic properties of Boolean algebras
cites work: Q3852172
cites work: Proper forcing
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description: scientific article; zbMATH DE number 513339