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Abstract: this paper, we will present a definability theorem for first order logic. This theorem is very easy to state, and its proof only uses elementary tools. To explain the theorem, let us first observe that if M is a model of a theory T in a language L, then, clearly, any definable subset S ae M (i.e., a subset S = fa j M j= '(a)g defined by some formula ') is invariant under all automorphisms of M . The same is of course true for subsets of M (Update)
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BibTeX entry: (Update)
@misc{ butz-elementary,
author = "C. Butz and I. Moerdijk",
title = "An Elementary Definability Theorem for First Order Logic",
url = "citeseer.ist.psu.edu/206399.html" }
Citations (may not include all citations):133 Cambridge University Press (context) - Hodges - 1993
83 Sheaves in Geometry and Logic (context) - Lane, Moerdijk - 1992
22 On Padoa's method in the theory of definition (context) - Beth - 1953
11 Logic with denumerably long formulas and finite strings of q.. (context) - Scott - 1965
4 Classifying toposes for first order theories - Butz, Johnstone - 1997
2 Representing topoi by topological groupoids - Butz, Moerdijk - 1996
2 Constructive sheaf semantics (context) - Palmgren - 1997
1 All topoi are localic or why permutation models prevail (context) - Freyd - 1987
1 Booleschewertige Logik (context) - Koppelberg - 1985
1 and semantics of infinitary languages (context) - Kueker, automorphisms et al. - 1968
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