标题： 基数特征与可数多个无限循环群的乘积 显示英文标题

标题： Cardinal Characteristics and the Product of Countably Many Infinite Cyclic Groups

摘要： 设 \( P \) 是可数多个整数加法群 \( \mathbb\{Z\} \) 的直积。 我们从集合论的角度研究 \( P \) 的那些子群，这些子群的所有同态到 \( \mathbb\{Z\} \) 都使所有标准单位向量中除了有限个以外的都变为零。 具体来说，我们将此类子群的最小可能大小与连续统的若干标准基数特性联系起来。 我们还研究了一些相关的性质和基数，这些性质既涉及群论也涉及集合论。 其中一个集合论性质及其对应的基数在组合上具有自然意义，与代数无关。 显示英文摘要

摘要： 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.