Abstracts: Boolean algebras

Author: Thomas Jech
Title: Algebraic characterizations of measure algebras
Proc. AMS 136 (2008)
Abstract: We present necessary and sufficient conditions for the existence of a countably additive measure on a complete Boolean algebra. For instance: the algebra is weakly distributive and uniformly concentrated.

Authors: Bohuslav Balcar and Thomas Jech
Title: Contributions to the theory of weakly distributive complete Boolean algebras
Andrzej Mostowski and Foundational Studies, IOS Press 2008
Abstract: We show, among others, that being a Maharam algebra is preserved under iteration.

Authors: Bohuslav Balcar and Thomas Jech
Title: Weak distributivity, a problem of von Neumann and the mystery of measurability
Bull. Symbolic Logic 12 (2006)
Abstract: We present a number of conditions equivalent to the property that a complete Boolean algebra carries a strictly positive Maharam submeasure.

Authors: Bohuslav Balcar, Thomas Jech and Tomas Pazak
Title: Complete ccc Boolean algebras, the order sequential topology, and a problem of von Neumann
Bull. London Math. Soc. 37 (2005)
Abstract: It is consistent that every weakly distributive complete ccc algebra carries a strictly positive Maharam submeasure.

Authors: Thomas Jech and Saharon Shelah
Title: Simple complete Boolean algebras
Proceedings AMS 129 (2001)
Abstract: We prove that for every regular cardinal there exists a simple complete Boolean algebra with as many generators.

Authors: Bohuslav Balcar, Wieslaw Glowczynski and Thomas Jech
Title: The sequential topology on complete Boolean algebras
Fundamenta Math. 155 (1998)
Abstract: We investigate the sequential topology on a complete Boolean algebra B determined by algebraically convergent sequences in B. We show the role of weak distributivity of B in separation axioms for the sequential topology. The main result is that a necessary and sufficient condition for B to carry a strictly positive Maharam submeasure is that B is ccc and that the sequential topology is Hausdorff. We also characterize sequential cardinals.

Authors: Bohuslav Balcar, Thomas Jech and Jindrich Zapletal
Title: Semi-Cohen Boolean algebras
Ann. Pure and Applied Logic 87 (1997)
Abstract: We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A Cohen algebra is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semi-Cohen algebras, pseudo-Cohen algebras and potentially Cohen algebras. These classes of Boolean algebras are closed under completion.

Authors: Thomas Jech and Saharon Shelah
Title: On countably closed complete Boolean algebras
J. Symb. Logic 61 (1996)
Abstract: It is unprovable that every complete subalgebra of a countably closed complete Boolean algebra is countably closed.

Authors: Thomas Jech and Saharon Shelah
Title: A complete Boolean algebra that has no proper atomless complete subalgebra
J. of Algebra 182 (1996)
Abstract: We prove that there exists a complete atomless Boolean algebra that has no proper atomless complete subalgebra.