8 found
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Peter T. Johnstone [7]Peter Johnstone [3]Peter A. K. Johnstone [1]
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  1.  30
    Classifying toposes for first-order theories.Carsten Butz & Peter Johnstone - 1998 - Annals of Pure and Applied Logic 91 (1):33-58.
    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 (...)
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  2. Methodology.Peter T. Johnstone & Steve Awodey - unknown
    Notices Amer. Math. Sac. 51, 2004). Logically, such a "Grothendieck topos" is something like a universe of continuously variable sets. Before long, however, F.W. Lawvere and M. Tierney provided an elementary axiomatization..
     
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  3. 2003 european summer meeting of the association for symbolic logic logic colloquim'03.Michael Benedikt, Stevo Todorcevic, Alexandru Baltag, Howard Becker, Matthew Foreman, Jean-Yves Girard, Martin Grohe, Peter T. Johnstone, Simo Knuuttila & Menachem Kojman - 2004 - Bulletin of Symbolic Logic 10 (2).
  4.  13
    Complemented sublocales and open maps.Peter T. Johnstone - 2006 - Annals of Pure and Applied Logic 137 (1-3):240-255.
    We show that a morphism of locales is open if and only if all its pullbacks are skeletal in the sense of [P.T. Johnstone, Factorization theorems for geometric morphisms, II, in: Categorical Aspects of Topology and Analysis, in: Lecture Notes in Math., vol. 915, Springer-Verlag, 1982, pp. 216–233], i.e. pulling back along them preserves denseness of sublocales . This result may be viewed as the ‘dual’ of the well-known characterization of proper maps as those which are stably closed. We also (...)
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  5.  22
    What do Freyd’s Toposes Classify?Peter Johnstone - 2013 - Logica Universalis 7 (3):335-340.
    We describe a method for presenting (a topos closely related to) either of Freyd’s topos-theoretic models for the independence of the axiom of choice as the classifying topos for a geometric theory. As an application, we show that no such topos can admit a geometric morphism from a two-valued topos satisfying countable dependent choice.
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  6.  15
    Ščedrov Andrej. Forcing and classifying topoi. Memoirs of the American Mathematical Society, no. 295. American Mathematical Society, Providence 1984, x + 93 pp. [REVIEW]Peter T. Johnstone - 1985 - Journal of Symbolic Logic 50 (3):852-853.
  7.  10
    Jaap van Oosten. Realizability: an introduction to its categorical side. Studies in Logic and the Foundations of Mathematics, vol. 152. Elsevier Science, Amsterdam, 2008, 328 pp. [REVIEW]Peter T. Johnstone - 2010 - Bulletin of Symbolic Logic 16 (3):407-409.
  8.  22
    Review: Andrej Scedrov, Forcing and Classifying Topoi. [REVIEW]Peter T. Johnstone - 1985 - Journal of Symbolic Logic 50 (3):852-853.