On Goodman Realizability

Notre Dame Journal of Formal Logic 60 (3):523-550 (2019)
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Abstract

Goodman’s theorem states that HAω+AC+RDC is conservative over HA. The same result applies to the extensional case, that is, E-HAω+AC+RDC is also conservative over HA. This is due to Beeson. In this article, we modified the Goodman realizability and provide a new proof of the extensional case.

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References found in this work

About Goodmanʼs Theorem.Thierry Coquand - 2013 - Annals of Pure and Applied Logic 164 (4):437-442.
Extended bar induction in applicative theories.G. R. Renardel Delavalette - 1990 - Annals of Pure and Applied Logic 50 (2):139-189.
Extended bar induction in applicative theories.Gerard R. Renardel de Lavalette - 1990 - Annals of Pure and Applied Logic 50 (2):139-189.
The theory of the Gödel functionals.Nicolas D. Goodman - 1976 - Journal of Symbolic Logic 41 (3):574-582.

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