Notre Dame Journal of Formal Logic

On Goodman Realizability

Emanuele Frittaion

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

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1562918420

Digital Object Identifier
doi:10.1215/00294527-2019-0018

Mathematical Reviews number (MathSciNet)
MR3985625

Zentralblatt MATH identifier
07120754

Subjects
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

Keywords
Goodman realizability axiom of choice extensionality

Citation

Frittaion, Emanuele. On Goodman Realizability. Notre Dame J. Formal Logic 60 (2019), no. 3, 523--550. doi:10.1215/00294527-2019-0018. https://projecteuclid.org/euclid.ndjfl/1562918420


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References

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    Digital Object Identifier: doi:10.1016/0168-0072(90)90047-6
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    Zentralblatt MATH: 06825026
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Duke University Press

Notre Dame Journal of Formal Logic

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