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Closed Normal Subgroups
Author(s) -
Schmerl James H.
Publication year - 2001
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200111)47:4<489::aid-malq489>3.0.co;2-8
Subject(s) - mathematics , peano axioms , pointwise , countable set , automorphism group , automorphism , elementary proof , invariant (physics) , discrete mathematics , pure mathematics , mathematical analysis , mathematical physics
Let ℳ be a countable, recursively saturated model of Peano Arithmetic, and let Aut(ℳ) be its automorphism group considered as a topological group with the pointwise stabilizers of finite sets being the basic open subgroups. Kaye proved that the closed normal subgroups are precisely the obvious ones, namely the stabilizers of invariant cuts. A proof of Kaye's theorem is given here which, although based on his proof, is different enough to yield consequences not obtainable from Kaye's proof.