Ultrafilters and Partial Products of Infinite Cyclic Groups

DOI10.1081/AGB-200063355zbMATH Open1089.03038arXivmath/0504199OpenAlexW2087500145MaRDI QIDQ5466669

S. Shelah, Andreas Blass

Publication date: 25 August 2005

Published in: Communications in Algebra (Search for Journal in Brave)

Abstract: We consider, for infinite cardinals kappa and alpha <= kappa^+, the group Pi(kappa,< alpha) of sequences of integers, of length kappa, with non-zero entries in fewer than alpha positions. Our main result tells when Pi(kappa,< alpha) can be embedded in Pi(lambda,< beta). The proof involves some set-theoretic results, one about familes of finite sets and one about families of ultrafilters.

Full work available at URL: https://arxiv.org/abs/math/0504199

zbMATH Keywords

Abelian groupsultrafilterproducts of groupsembeddings of groups

Mathematics Subject Classification ID

Torsion-free groups, infinite rank (20K20) Other combinatorial set theory (03E05) Direct sums, direct products, etc. for abelian groups (20K25) Ordinal and cardinal numbers (03E10)

Cites Work

• Title not available (Why is that?)
• Verallgemeinerung eines Satzes von Herrn F. Specker
• Special Families of Sets and Baer-Specker Groups

Related Items (3)

Ultraproducts, \(p\)-limits and antichains on the Comfort group order ⋮ Families of ultrafilters, and homomorphisms on infinite direct product algebras ⋮ Ultrafilters and decompositions of Abelian groups

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