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A categorical version of the Brouwer–Heyting–Kolmogorov interpretation

Published online by Cambridge University Press:  03 February 2004

ERIK PALMGREN
ERIK PALMGREN
Affiliation:
Department of Mathematics, Uppsala University, PO Box 480, SE-751 06 Uppsala, Sweden Email: palmgren@math.uu.se
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Abstract

In this paper we interpret (fragments of) intuitionistic logic in categories with weak closure properties, such as quasi left exact categories and locally cartesian closed categories (LCCC) with sums. We also interpret the full choice scheme in an LCCC. The interpretation can be seen as a categorical form of the usual Brouwer–Heyting– Kolmogorov (BHK) interpretation. The standard interpretation of geometric logic in a pretopos is obtained by applying the image functor to the BHK-interpretation.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 14 , Issue 1 , February 2004 , pp. 57 - 72
Copyright
2004 Cambridge University Press

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