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The Journal of Symbolic Logic The Journal of Symbolic Logic

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On countably closed complete Boolean algebras

Published online by Cambridge University Press:  12 March 2014

Thomas Jech  and
Saharon Shelah
Thomas Jech
Affiliation:
Department of Mathematics, The Pennsylvania State University, University Park, PA 16803, USA, E-mail: jech@math.psu.edu
Saharon Shelah
Affiliation:
School of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA, E-mail: shelah@sunrise.huji.ac.ilshelah@math.rutgers.edu
Corresponding
E-mail address:
jech@math.psu.edu
shelah@sunrise.huji.ac.il
shelah@math.rutgers.edu
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Abstract

It is unprovable that every complete subalgebra of a countably closed complete Boolean algebra is countably closed.

Keywords

Boolean algebra countably closed game-closed forcing
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 4 , December 1996 , pp. 1380 - 1386
Copyright
Copyright © Association for Symbolic Logic 1996

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References

[1]Foreman, M., Games played on Boolean algebras, this Journal, vol. 48 (1983), pp. 714–723.Google Scholar
[2]Jech, T., A game-theoretic property of Boolean algebras, (Macintyre, A.et al., editors), Logic Colloquium 77, North-Holland, Amsterdam, 1978, pp. 135–144.Google Scholar
[3]Jech, T., More game-theoretic properties of Boolean algebras, Annals of Pure and Applied Logic, vol. 26 (1984), pp. 11–29.CrossRefGoogle Scholar
[4]Veličković, B., Playful Boolean algebras, Transactions of the American Mathematical Society, vol. 296 (1986), pp. 727–740.CrossRefGoogle Scholar
[5]Vojtáš, P., Game properties of Boolean algebras, Comment. Math. Univ. Carol., vol. 24 (1983), pp. 349–369.Google Scholar

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