To the top

Page Manager: Webmaster
Last update: 9/11/2012 3:13 PM

Tell a friend about this page
Print version

Invariance and Definabili… - University of Gothenburg, Sweden Till startsida
Sitemap
To content Read more about how we use cookies on gu.se

Invariance and Definability, with and without Equality

Journal article
Authors Dennis Bonnay
Fredrik Engström
Published in Notre Dame Journal of Formal Logic
Volume 59
Issue 1
Pages 109-133
ISSN 0029-4527
Publication year 2018
Published at Department of Philosophy, Linguistics and Theory of Science
Pages 109-133
Language en
Links dx.doi.org/10.1215/00294527-2017-00...
Keywords generalized quantifiers infinite languages invariance definability automorphism groups equality-free languages
Subject categories Mathematical logic, Logic

Abstract

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 L∞∞L∞∞ 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 L∞∞L∞∞ 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.

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

The University of Gothenburg uses cookies to provide you with the best possible user experience. By continuing on this website, you approve of our use of cookies.  What are cookies?