First order theory of permutation groups

Saharon Shelah

doi:10.1007/BF02762670

First order theory of permutation groups

Saharon Shelah^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

21 Scopus citations

Abstract

We solve the problem of the elementary equivalence (definability) of the permutation groups over cardinals א_α. 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 < (2^א₀)⁺. We solve a problem of Mycielski and McKenzie on embedding of free groups in permutation groups, and discuss some weak second-order quantifiers.

Original language	English
Pages (from-to)	149-162
Number of pages	14
Journal	Israel Journal of Mathematics
Volume	14
Issue number	2
DOIs	https://doi.org/10.1007/BF02762670
State	Published - Jun 1973

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First order theory of permutation groups

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