Implausible Subgroups of Infinite Symmetric Groups
Copyright policy )Implausible Subgroups of Infinite Symmetric Groups
Let S denote the infinite symmetric group of all permutations of \(\omega\), the set of natural numbers. The authors study the possibilities for the induced action of subgroups \(G\subseteq S\) on the power set \({\mathcal P}(\omega)\). Assuming Martin's axiom (MA), they show, in particular, that for any infinite cardinal \(\kappa \theta\), Sym(\(\kappa)\) does not embed in Sym(\(\theta)\).
- Rutgers, The State University of New Jersey United States
- Hebrew University of Jerusalem Israel
- University of New Brunswick Canada
Subgroups of symmetric groups, Models with special properties (saturated, rigid, etc.), infinite symmetric group, power set, Martin's axiom, orbits, Logical aspects of Boolean algebras, induced action of subgroups
Subgroups of symmetric groups, Models with special properties (saturated, rigid, etc.), infinite symmetric group, power set, Martin's axiom, orbits, Logical aspects of Boolean algebras, induced action of subgroups
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