Notre Dame Journal of Formal Logic

On Goodman Realizability

Emanuele Frittaion

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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 modify Goodman realizability and provide a new proof of the extensional case.

Article information

Notre Dame J. Formal Logic, Volume 60, Number 3 (2019), 523-550.

Received: 8 November 2017
Accepted: 8 March 2018
First available in Project Euclid: 12 July 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03F03: Proof theory, general
Secondary: 03F10: Functionals in proof theory 03F30: First-order arithmetic and fragments 03F35: Second- and higher-order arithmetic and fragments [See also 03B30] 03F50: Metamathematics of constructive systems

Goodman realizability axiom of choice extensionality


Frittaion, Emanuele. On Goodman Realizability. Notre Dame J. Formal Logic 60 (2019), no. 3, 523--550. doi:10.1215/00294527-2019-0018.

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