Classifying toposes for first-order theories

Annals of Pure and Applied Logic 91 (1):33-58 (1998)

Abstract
By a classifying topos for a first-order theory , we mean a topos such that, for any topos models of in correspond exactly to open geometric morphisms → . We show that not every 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
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DOI 10.1016/s0168-0072(97)00042-0
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References found in this work BETA

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