Classifying topoi and finite forcing

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Classifying topoi and finite forcing

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Elsevier

Abstract

We show that Robinson's finite forcing, for a theory , is a universal construction in the sense of categorical algebra: it is the satisfaction relation for the universal model in the classifying topos of a certain universal Horn theory defined from . Assuming, without loss of generality, that is axiomatized by universal sentences, we construct, as sheaf subtopoi of , the classifying topoi for (i.e., universal examples of) finitely generic models, existentially closed models, and arbitrary models of (with complemented primitive predicates).

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