The Affinity of Set Theory and Abelian Group Theory

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This paper reviews the uses of set theory to solve some long-standing problems in a number of different areas of abelian group theory. In some cases the solution is an independence result (from ZFC, the ordinary axioms of set theory); in other cases the result is a theorem of ZFC proved by combinatorial methods. In the interests of breadth, and to keep within the prescribed bounds of space, some depth and detail have been sacrificed and the emphasis is on key developments in the early history of each area. In general, except for Butler groups, a cut-off date of about 1990 has been observed, except for brief references to selected later developments. Also, for reasons of space, the bibliography is not complete.