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Interpreting descriptions in intensional type theory

Published online by Cambridge University Press:  12 March 2014

Jesper Carlström
Jesper Carlström*
Affiliation:
Department of Mathematics, Stockholm University, Stockholm., Sweden, URL: http://www.math.su.se/~jesper
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Abstract

Natural deduction systems with indefinite and definite descriptions (ε-terms and ι-terms) are presented, and interpreted in Martin-LÖf's intensional type theory. The interpretations are formalizations of ideas which are implicit in the literature of constructive mathematics: if we have proved that an element with a certain property exists, we speak of ‘the element such that the property holds’ and refer by that phrase to the element constructed in the existence proof. In particular, we deviate from the practice of interpreting descriptions by contextual definitions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 70 , Issue 2 , June 2005 , pp. 488 - 514
Copyright
Copyright © Association for Symbolic Logic 2005

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