**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.