Abstract
There is a natural map which assigns to every modelU of typeτ, (U ε Stτ) a groupG (U) in such a way that elementarily equivalent models are mapped into isomorphic groups.G(U) is a subset of a collection whose members are called Fraisse arrows (they are decreasing sequences of sets of partial isomorphisms) and which arise in connection with the Fraisse characterization of elementary equivalence. LetEC Uλ be defined as {U εStr τ: ℬ ≡U and |ℬ|=λ; thenEG Uλ can be faithfully (i.e. 1-1) represented onto G(U) ×π *, whereπ *, is a collection of partitions over λ∪λ2∪....
References
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R. Fraisse,Sur quelques classifications des systèmes de relations,Publ. Sci. Univ. Alger Ser. A1 35–182 (1954).
J. Flum,First order logic and its extensions,Lecture Notes in Mathematics 499 (1975), pp. 248–310.
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Mundici, D. A group-theoretical invariant for elementary equivalence and its role in representations of elementary classes. Stud Logica 40, 253–267 (1981). https://doi.org/10.1007/BF02584060
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DOI: https://doi.org/10.1007/BF02584060