First order theory of permutation groups

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

We solve the problem of the elementary equivalence (definability) of the permutation groups over cardinals אα. We show that it suffices to solve the problem of elementary equivalence (definability) for the ordinals α in certain second order logic, and this is reduced to the case of α < (2א 0)+. We solve a problem of Mycielski and McKenzie on embedding of free groups in permutation groups, and discuss some weak second-order quantifiers.

Original languageEnglish
Pages (from-to)149-162
Number of pages14
JournalIsrael Journal of Mathematics
Volume14
Issue number2
DOIs
StatePublished - Jun 1973

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