• Corpus ID: 17759696

# Non-permutation invariant Borel quantifiers

@article{Engstrom2010NonpermutationIB,
title={Non-permutation invariant Borel quantifiers},
author={F. Brett Engstrom and Philipp Schlicht},
journal={arXiv: Logic},
year={2010}
}
• Published 12 March 2010
• Mathematics
• arXiv: 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…

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