STACKED BASES FOR COUNTABLE HOMOGENEOUS COMPLETELY DECOMPOSABLE GROUPS

Abstract

Let A ⊆ X be two homogeneous completely decomposable torsion free abelian groups of the same type τ and of countable rank such that the quotient X/A is a direct sum of torsion cyclic groups and a homogeneous completely decomposable summand of type τ. Furthermore assume that A and X have a common direct summand of countable rank. We show that there exist stacked bases for A and X, i.e. there exist xi ∈ X (i ∈ ω) and di ∈ Z (i ∈ ω) such that and . This proves a stacked bases theorem for pairs of homogeneous completely decomposable torsion free abelian groups of countable rank and the same type with a large commmon summand.