• Corpus ID: 17759696

Non-permutation invariant Borel quantifiers

  title={Non-permutation invariant Borel quantifiers},
  author={F. Brett Engstrom and Philipp Schlicht},
  journal={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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