A representation theorem for languages with generalized quantifiers through back-and-forth methods

Studia Logica 47 (4):401 - 411 (1988)
Abstract
We obtain in this paper a representation of the formulae of extensions ofL by generalized quantifiers through functors between categories of first-order structures and partial isomorphisms. The main tool in the proofs is the back-and-forth technique. As a corollary we obtain the Caicedo's version of Fraïssés theorem characterizing elementary equivalence for such languages. We also discuss informally some geometrical interpretations of our results.
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