Classifying toposes for first-order theories

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

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

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 90,616

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

What do Freyd’s Toposes Classify?Peter Johnstone - 2013 - Logica Universalis 7 (3):335-340.
Syntax and Semantics of the Logic.Carsten Butz - 1997 - Notre Dame Journal of Formal Logic 38 (3):374-384.
The uses and abuses of the history of topos theory.Colin Mclarty - 1990 - British Journal for the Philosophy of Science 41 (3):351-375.
The Skolem-löwenheim theorem in toposes.Marek Zawadowski - 1983 - Studia Logica 42 (4):461 - 475.

Analytics

Added to PP
2014-01-16

Downloads
25 (#542,984)

6 months
2 (#668,348)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Citations of this work

A syntactic characterization of Morita equivalence.Dimitris Tsementzis - 2017 - Journal of Symbolic Logic 82 (4):1181-1198.
Infinitary first-order categorical logic.Christian Espíndola - 2019 - Annals of Pure and Applied Logic 170 (2):137-162.
Saturated models of intuitionistic theories.Carsten Butz - 2004 - Annals of Pure and Applied Logic 129 (1-3):245-275.

View all 11 citations / Add more citations

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.

View all 10 references / Add more references