Some properties of Boolean algebras are characterized through the topological properties of a certain space of countable sequences of ordinals. For this, it is necessary to prove the Ramsey theorems for an arbitrary infinite cardinal. Also, we define continuous mappings on these spaces from vector measures on the algebra.
The Open Colouring Axiom implies that the measure algebra cannot be embedded into P(ℕ)/fin. We also discuss errors in previous results on the embeddability of the measure algebra.
There is a conjecture of Vaught [17] which states: Without The Generalized Continuum Hypothesis one can prove the existence of a complete theory with exactly nonisomorphic, denumerable models. In this paper we show that there is no such theory in the class of complete extensions of the theory of Boolean algebras. More precisely, any complete extension of the theory of Boolean algebras has either 1 or nonisomorphic, countable models. Thus we answer this conjecture in the negative for any complete...
In this paper we investigate the relations between torsion classes of Specker lattice ordered groups and torsion classes of generalized Boolean algebras.