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Non-permutation invariant Borel quantifiers

Magazine article
Authors Fredrik Engström
Philipp Schlicht
Published in Insitut Mittag-Leffler preprint serie
Issue REPORT No. 23, 2009/2010
Pages 10
ISSN 1103-467X
Publication year 2010
Published at Department of Philosophy, Linguistics and Theory of Science
Pages 10
Language en
Links www.mittag-leffler.se/preprints/fil...
Subject categories Mathematical logic, Logic

Abstract

Every permutation invariant Borel subset of the space of countable structures is definable in $\La_{\omega_1\omega}$ by a theorem of Lopez-Escobar. We prove variants of this theorem relative to fixed relations and fixed non-permutation invariant quantifiers. Moreover we show that for every closed subgroup $G$ of the symmetric group $S_{\infty}$, there is a closed binary quantifier $Q$ such that the $G$-invariant subsets of the space of countable structures are exactly the $\La_{\omega_1\omega}(Q)$-definable sets.

Page Manager: Webmaster|Last update: 9/11/2012
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