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Ultrafilters and partial products of infinite cyclic groups

Research paper by Andreas Blass, Saharon Shelah

Indexed on: 10 Apr '05Published on: 10 Apr '05Published in: Mathematics - Logic



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.