A group-theoretical invariant for elementary equivalence and its role in representations of elementary classes

Studia Logica 40 (3):253 - 267 (1981)
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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 λ U be defined as {U εStr τ: ℬ ≡U and |ℬ|=λ; thenEG λ U can be faithfully (i.e. 1-1) represented onto G(U) ×π *, whereπ *, is a collection of partitions over λ∪λ2∪..

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