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Krivine's classical realisability from a categorical perspective

Published online by Cambridge University Press:  10 April 2013

THOMAS STREICHER
THOMAS STREICHER*
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, 64289 Darmstadt, Germany Email: [email protected]
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Abstract

In a sequence of papers (Krivine 2001; Krivine 2003; Krivine 2009), J.-L. Krivine introduced his notion of classical realisability for classical second-order logic and Zermelo–Fraenkel set theory. Moreover, in more recent work (Krivine 2008), he has considered forcing constructions on top of it with the ultimate aim of providing a realisability interpretation for the axiom of choice.

The aim of the current paper is to show how Krivine's classical realisability can be understood as an instance of the categorical approach to realisability as started by Martin Hyland in Hyland (1982) and described in detail in van Oosten (2008). Moreover, we will give an intuitive explanation of the iteration of realisability as described in Krivine (2008).

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 23 , Issue 6 , December 2013 , pp. 1234 - 1256
Copyright
Copyright © Cambridge University Press 2013 

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