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A Constructive Model of Uniform Continuity

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7941)

Abstract

We construct a continuous model of Gödel’s system T and its logic HA ω in which all functions from the Cantor space 2 to the natural numbers are uniformly continuous. Our development is constructive, and has been carried out in intensional type theory in Agda notation, so that, in particular, we can compute moduli of uniform continuity of T-definable functions 2 → ℕ. Moreover, the model has a continuous Fan functional of type (2 → ℕ) → ℕ that calculates moduli of uniform continuity. We work with sheaves, and with a full subcategory of concrete sheaves that can be presented as sets with structure, which can be regarded as spaces, and whose natural transformations can be regarded as continuous maps.

Keywords

Constructive mathematics topological models uniform continuity Fan functional intuitionistic type theory topos theory sheaves HAω Gödel’s system T 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University of BirminghamUK

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