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Intensional interpretations of functionals of finite type I

Published online by Cambridge University Press:  12 March 2014

W. W. Tait*
Affiliation:
Stanford University

Extract

T0 will denote Gödel's theory T[3] of functionals of finite type (f.t.) with intuitionistic quantification over each f.t. added. T1 will denote T0 together with definition by bar recursion of type o, the axiom schema of bar induction, and the schema

of choice. Precise descriptions of these systems are given below in §4. The main results of this paper are interpretations of T0 in intuitionistic arithmetic U0 and of T1 in intuitionistic analysis is U1. U1 is U0 with quantification over functionals of type (0,0) and the axiom schemata AC00 and of bar induction.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1967

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References

[1]Brouwer, L. E. J., Über Definitionsbereiche von Funktionen, Mathematische Annalen, vol. 97 (1927), pp. 6076.CrossRefGoogle Scholar
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[10]Tait, W. W., A second order theory of functionals of higher type (to appear).Google Scholar
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