Journal of Symbolic Logic

The axiom of choice and combinatory logic

Andrea Cantini

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We combine a variety of constructive methods (including forcing, realizability, asymmetric interpretation), to obtain consistency results concerning combinatory logic with extensionality and (forms of) the axiom of choice.

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J. Symbolic Logic, Volume 68, Issue 4 (2003), 1091-1108.

First available in Project Euclid: 31 October 2003

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Primary: 03B40: Combinatory logic and lambda-calculus [See also 68N18] 03B55: Intermediate logics 03F50: Metamathematics of constructive systems 03F25: Relative consistency and interpretations 03F05: Cut-elimination and normal-form theorems


Cantini, Andrea. The axiom of choice and combinatory logic. J. Symbolic Logic 68 (2003), no. 4, 1091--1108. doi:10.2178/jsl/1067620175.

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