CARDINAL CHARACTERISTICS AND THE PRODUCT OF COUNTABLY MANY INFINITE CYCLIC GROUPS

[摘要] We study, from a set-theoretic point of view, those subgroups of the infinite direct product Z(N0) for which all homomorphisms to Z 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. (C) 1994 Academic Press, Inc.

[发布日期] 1994-10-15