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The dual character of invariance under transformations and definability by some operations has been used in classical works by, for example, Galois and Klein. Following Tarski, philosophers of logic have claimed that logical notions themselves could be characterized in terms of invariance. In this article, we generalize a correspondence due to Krasner between invariance under groups of permutations and definability in $\mathscr{L}_{\infty\infty}$ so as to cover the cases (quantifiers, logics without equality) that are of interest in the logicality debates, getting McGee’s theorem about quantifiers invariant under all permutations and definability in pure $\mathscr{L}_{\infty\infty}$ as a particular case. We also prove some optimality results along the way, regarding the kinds of relations which are needed so that every subgroup of the full permutation group is characterizable as a group of automorphisms.

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Project Euclid (Hosted at Cornell University Library)  


Bonnay, Denis -  Engström, Fredrik - 

Id.: 70828095

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras clavegeneralized quantifiers - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 University of Notre Dame

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 0029-4527
[References] 1939-0726

Fecha de contribución: 17-mar-2018


* Notre Dame J. Formal Logic 59, no. 1 (2018), 109-133
* doi:10.1215/00294527-2017-0020

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