Finite Sets and Natural Numbers in Intuitionistic TT

Notre Dame Journal of Formal Logic 37 (4):585-601 (1996)
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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, 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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New Foundations for Mathematical Logic.W. V. Quine - 1937 - Journal of Symbolic Logic 2 (2):86-87.
A set of axioms for logic.Theodore Hailperin - 1944 - Journal of Symbolic Logic 9 (1):1-19.
Models of intuitionistic TT and N.Daniel Dzierzgowski - 1995 - Journal of Symbolic Logic 60 (2):640-653.
Arithmetic and the theory of types.M. Boffa - 1984 - Journal of Symbolic Logic 49 (2):621-624.

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