Classifying toposes for first-order theories

Annals of Pure and Applied Logic 91 (1):33-58 (1998)
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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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References found in this work

Sheaves and Logic.M. P. Fourman, D. S. Scott & C. J. Mulvey - 1983 - Journal of Symbolic Logic 48 (4):1201-1203.
La logique Des topos.André Boileau & André Joyal - 1981 - Journal of Symbolic Logic 46 (1):6-16.
Minimal models of Heyting arithmetic.Ieke Moerdijk & Erik Palmgren - 1997 - Journal of Symbolic Logic 62 (4):1448-1460.
Constructive Sheaf Semantics.Erik Palmgren - 1997 - Mathematical Logic Quarterly 43 (3):321-327.
Infinitary intuitionistic logic from a classical point of view.Mark E. Nadel - 1978 - Annals of Mathematical Logic 14 (2):159-191.

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