Abstract
This paper is about the combinatorial properties necessary for the construction of realizability models with certain type-theoretic properties. We take as our basic construction a form of tagging in which elements of sets are equipped with tags, and functions must operate constructively on tags. To complete the construction we allow a form of closure under quotients by equivalence relations. In this paper we analyse first the condition for a natural monoidal structure to be product structure, and then investigate necessary conditions for the realizability model to be locally cartesian closed and to have a subobject classifier.
The authors wish to acknowledge the support of the EPSRC, EU Working Group 26142 APPSEM, and MURST
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Robinson, E., Rosolini, G. (2001). An Abstract Look at Realizability. In: Fribourg, L. (eds) Computer Science Logic. CSL 2001. Lecture Notes in Computer Science, vol 2142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44802-0_13
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DOI: https://doi.org/10.1007/3-540-44802-0_13
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