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 language | English |
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Pages (from-to) | 149-162 |
Number of pages | 14 |
Journal | Israel Journal of Mathematics |
Volume | 14 |
Issue number | 2 |
DOIs | |
State | Published - Jun 1973 |