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Fall 1996 Finite Sets and Natural Numbers in Intuitionistic TT
Daniel Dzierzgowski
Notre Dame J. Formal Logic 37(4): 585-601 (Fall 1996). DOI: 10.1305/ndjfl/1040046143

Abstract

We show how to interpret Heyting's arithmetic in an intuitionistic version of TT, Russell's Simple Theory of Types. We also exhibit properties of finite sets in this theory and compare them with the corresponding properties in classical TT. Finally, we prove that arithmetic can be interpreted in intuitionistic TT$_3$, the subsystem of intuitionistic TT involving only three types. The definitions of intuitionistic TT and its finite sets and natural numbers are obtained in a straightforward way from the classical definitions. This is very natural and seems to make intuitionistic TT an interesting intuitionistic set theory to study, beside intuitionistic ZF.

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Daniel Dzierzgowski. "Finite Sets and Natural Numbers in Intuitionistic TT." Notre Dame J. Formal Logic 37 (4) 585 - 601, Fall 1996. https://doi.org/10.1305/ndjfl/1040046143

Information

Published: Fall 1996
First available in Project Euclid: 16 December 2002

zbMATH: 0882.03049
MathSciNet: MR1446230
Digital Object Identifier: 10.1305/ndjfl/1040046143

Subjects:
Primary: 03B15
Secondary: 03F30

Rights: Copyright © 1996 University of Notre Dame

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Vol.37 • No. 4 • Fall 1996
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