Quotient divisible abelian groups

On the Divisible Parts of Quotient Groups

We study the possible cardinalities of the divisible part of G/K when the cardinality of K is known and when, for all countable subgroups C of G, the divisible part of G/C is countable.

Interpreting Formulas of Divisible Lattice Ordered Abelian Groups - Preliminary Version

We show that a large class of divisible abelian `-groups (lattice ordered groups) of continuous functions is interpretable (in a certain sense) in the lattice of the zero sets of these functions. This has various applications to the model theory of these `-groups, including decidability results.

A Superposition Calculus for Divisible Torsion-Free Abelian Groups

Weakly infinitely divisible measures on some locally compact Abelian groups

Let G be a locally compact Abelian topological group having a countable basis of its topology. We also suppose that G has the T0–property, that is, ⋂ U∈Ne U = {e}, where e denotes the identity element of G and Ne is the collection of all Borel neighbourhoods of e. (By a Borel neighbourhood U of e we mean a Borel subset of G for which there exists an open subset Ũ of G such that e ∈ Ũ ⊂ U.) Let ...

On Compact Divisible Abelian Semigroups

The algebraic structure of divisible abelian semigroups has been studied in [9] and [l]. Some results on the topological and algebraic structure of compact uniquely divisible abelian semigroups have been obtained in [4] and [5]. A statement of equivalent conditions for a compact abelian semigroup to be divisible is presented in the present paper. Some of the results in [4] are extended to subun...