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Title of article :
Classifying toposes for first-order theories Original Research Article
Author/Authors :
Carsten Butz، نويسنده , , Peter Johnstone، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 1998
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Abstract :
By a classifying topos for a first-order theory View the MathML source, we mean a topos ∄ such that, for any topos View the MathML source models of View the MathML source in View the MathML source correspond exactly to open geometric morphisms View the MathML source → View the MathML source. We show that not every (infinitary) first-order theory has a classifying topos in this sense, but we characterize those which do by an appropriate ‘smallness condition’, and we show that every Grothendieck topos arises as the classifying topos of such a theory. We also show that every first-order theory has a conservative extension to one which possesses a classifying topos, and we obtain a Heyting-valued completeness theorem for infinitary first-order logic.
Keywords :
Classifying topos , First-order theory
Journal title :
Annals of Pure and Applied Logic
Serial Year :
Link To Document :