Journal of Symbolic Logic

The axiom of choice and combinatory logic

Andrea Cantini

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 31 October 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1067620175

Digital Object Identifier
doi:10.2178/jsl/1067620175

Mathematical Reviews number (MathSciNet)
MR2017343

Zentralblatt MATH identifier
1063.03007

Subjects
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

Citation

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


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