Author: Thomas Jech
Title: Convergence and submeasures in Boolean algebras
preprint
Abstract:
We present necessary and sufficient condition for the existence of an exhaustive
submeasure on a Boolean algebra.
Author: Thomas Jech
Title: Measures on Boolean algebras
Fundamenta Math.
Abstract:
We present necessary and sufficient condition for the existence of a finitely
additive measure on a Boolean algebra.
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.