Cardinal Characteristics and the Product of Countably Many Infinite Cyclic Groups

Andreas Blass

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arXiv · math/9209203

Cardinal Characteristics and the Product of Countably Many Infinite Cyclic Groups

Andreas Blass

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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.

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BibTeX RIS

Andreas Blass. 1992-09-08. Cardinal Characteristics and the Product of Countably Many Infinite Cyclic Groups. https://arxiv.org/abs/math/9209203

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