Cardinal Characteristics and the Product of Countably Many Infinite Cyclic Groups Original Research Article

We study, from a set-theoretic point of view, those subgroups of the infinite direct product imagealeph, Hebrew0 for which all homomorphisms to image annihilate all but finitely many of the standard unit vectors. Specifically, we relate the smallest possible size of such a subgroup to several of the standard cardinal characteristics of the continuum. We also study some related properties and cardinals, both group-theoretic and set-theoretic. One of the set-theoretic properties and the associated cardinal are combinatorially natural, independently of any connection with algebra.