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Hilbert's ϵ-operator in intuitionistic type theories

✍ Scribed by John L. Bell

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
702 KB
Volume
39
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

We investigate Hilbert's ϵ‐calculus in the context of intuitionistic type theories, that is, within certain systems of intuitionistic higher‐order logic. We determine the additional deductive strength conferred on an intuitionistic type theory by the adjunction of closed ϵ‐terms. We extend the usual topos semantics for type theories to the ϵ‐operator and prove a completeness theorem. The paper also contains a discussion of the concept of “partially defined” ϵ‐term. MSC: 03B15, 03B20, 03G30.

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