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An algebraic result about soft model theoretical equivalence relations with an application to H. Friedman's fourth problem

Published online by Cambridge University Press:  12 March 2014

Daniele Mundici
Daniele Mundici*
Affiliation:
Loc. Romola N. 76, 50060 Donnini, Florence, Italy
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Abstract

We prove the following algebraic characterization of elementary equivalence: ≡ restricted to countable structures of finite type is minimal among the equivalence relations, other than isomorphism, which are preserved under reduct and renaming and which have the Robinson property; the latter is a faithful adaptation for equivalence relations of the familiar model theoretical notion. We apply this result to Friedman's fourth problem by proving that if is an (ω1, ω)-compact logic satisfying both the Robinson consistency theorem on countable structures of finite type and the Löwenheim-Skolem theorem for some λ < ωω for theories having ω1 many sentences, then ≡L = ≡ on such structures.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 46 , Issue 3 , September 1981 , pp. 523 - 530
Copyright
Copyright © Association for Symbolic Logic 1981

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References

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