## Notre Dame Journal of Formal Logic

### On Goodman Realizability

Emanuele Frittaion

#### Abstract

Goodman’s theorem states that $\mathsf{HA}^{\omega }+{\mathsf{AC}}+{\mathsf{RDC}}$ is conservative over ${\mathsf{HA}}$. The same result applies to the extensional case, that is, ${\mathsf{E}}\text{-}{\mathsf{HA}}^{\omega}+{\mathsf{AC}}+{\mathsf{RDC}}$ is also conservative over ${\mathsf{HA}}$. 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
Accepted: 8 March 2018
First available in Project Euclid: 12 July 2019

https://projecteuclid.org/euclid.ndjfl/1562918420

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

Mathematical Reviews number (MathSciNet)
MR3985625

Zentralblatt MATH identifier
07120754

#### 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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