The Existence of Large ω1-Homogeneous But Not ω-Homogeneous Permutation Groups is Consistent with Zfc+Gch

S. Shelah*, L. Soukup

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Denote by Perm (λ) the group of all permutations of a cardinal λ. A subgroup G of Perm (λ) is called K-homogeneous if and only if for all X, Y € [λ]K there is a g € G with g″X = Y. We show that if either (i) ⋄+ holds and we add ω1 Cohen reals to the ground model, or (ii) we add 2ω1 Cohen reals to the ground model, then in the generic extension for each λ ≥ ω2 there is an ω1-homogeneous subgroup of Perm (λ) which is not ω-homogeneous.

Original languageEnglish
Pages (from-to)193-203
Number of pages11
JournalJournal of the London Mathematical Society
Volumes2-48
Issue number2
DOIs
StatePublished - Oct 1993

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