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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
Subject categories Mathematical logic, Logic


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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