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Interpreting classical theories in constructive ones
Journal of Symbolic Logic 65 (4):1785-1812 (2000)
Abstract
A number of classical theories are interpreted in analogous theories that are based on intuitionistic logic. The classical theories considered include subsystems of first- and second-order arithmetic, bounded arithmetic, and admissible set theory.Author's Profile
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Citations of this work
A marriage of Brouwer’s intuitionism and Hilbert’s finitism I: Arithmetic.Takako Nemoto & Sato Kentaro - 2022 - Journal of Symbolic Logic 87 (2):437-497.
Very Large Set Axioms Over Constructive Set Theories.Hanul Jeon & Richard Matthews - 2024 - Bulletin of Symbolic Logic 30 (4):455-535.
Saturated models of universal theories.Jeremy Avigad - 2002 - Annals of Pure and Applied Logic 118 (3):219-234.
References found in this work
The Type Theoretic Interpretation of Constructive Set Theory.Peter Aczel, Angus Macintyre, Leszek Pacholski & Jeff Paris - 1984 - Journal of Symbolic Logic 49 (1):313-314.
The strength of some Martin-Löf type theories.Edward Griffor & Michael Rathjen - 1994 - Archive for Mathematical Logic 33 (5):347-385.
The consistency of classical set theory relative to a set theory with intuitionistic logic.Harvey Friedman - 1973 - Journal of Symbolic Logic 38 (2):315-319.
Functional interpretations of feasibly constructive arithmetic.Stephen Cook & Alasdair Urquhart - 1993 - Annals of Pure and Applied Logic 63 (2):103-200.
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