Abstract
In this paper, we prove that Heyting's arithmetic can be interpreted in an intuitionistic version of Russell's Simple Theory of Types without extensionality.
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References
Boffa, M., ‘The point on Quine's NF’ (with a bibliography), Teoria IV/2:3–13, 1984.
Dzierzgowski, D., ‘Finite sets and natural numbers in intuitionistic TT’, Notre Dame Journal of Formal Logic 37(4): 585–601, 1996.
Dzierzgowski, D., ‘Models of intuitionistic TT and NF’, Journal of Symbolic Logic, 60(2):640–653, June 1995.
Forster, T. E., Set theory with a universal set. Exploring an untyped universe, volume 20 of Oxford Logic Guides, Clarendon Press, Oxford University Press, 1992.
Fraenkel, A. A., Y. Bar-Hillel, and A. Llevy, Foundations of Set Theory, volume 67 of Studies in logic and the foundations of mathematics, North-Holland Publishing Company, 1973.
Myhill, J., ‘Some properties of intuitionistic Zermelo-Fraenkel set theory’, in Cambridge Summer School in Mathematical Logic, volume 337 of Lecture Notes in Mathematics, p. 206–231, Springer-Verlag, 1973.
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Dzierzgowski, D. Finite Sets and Natural Numbers in Intuitionistic TT Without Extensionality. Studia Logica 61, 417–428 (1998). https://doi.org/10.1023/A:1005022208588
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DOI: https://doi.org/10.1023/A:1005022208588