Cardinal Characteristics and the Product of Countably Many Infinite Cyclic Groups
Logic
2009-09-25 v1
Abstract
Let P be the direct product of countably many copies of the additive group Z of integers. We study, from a set-theoretic point of view, those subgroups of P 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.
Cite
@article{arxiv.math/9209203,
title = {Cardinal Characteristics and the Product of Countably Many Infinite Cyclic Groups},
author = {Andreas Blass},
journal= {arXiv preprint arXiv:math/9209203},
year = {2009}
}