Journal of Symbolic Logic 65 (3):1168-1182 (2000)

Authors
Steve Awodey
Carnegie Mellon University
Abstract
Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces- so -called "topological semantics." The first is classical higher-order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over arbitrary relations. The second theorem applies to intuitionistic as well as classical logic
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DOI 10.2307/2586693
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References found in this work BETA

Completeness in the Theory of Types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.
A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.
Introduction to Higher Order Categorical Logic.J. Lambek & P. J. Scott - 1989 - Journal of Symbolic Logic 54 (3):1113-1114.
A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (3):114-115.
La Logique Des Topos.André Boileau & André Joyal - 1981 - Journal of Symbolic Logic 46 (1):6-16.

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Citations of this work BETA

Category Theory.Jean-Pierre Marquis - 2008 - Stanford Encyclopedia of Philosophy.
What is Categorical Structuralism?Geoffrey Hellman - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 151--161.
Topological Completeness of First-Order Modal Logics.Steve Awodey & Kohei Kishida - 2012 - In Thomas Bolander, Torben Braüner, Silvio Ghilardi & Lawrence Moss (eds.), Advances in Modal Logic, Volume 9. CSLI Publications. pp. 1-17.

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