Intuitionistically provable recursive well-orderings

Annals of Pure and Applied Logic 30 (2):165-171 (1986)
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Abstract

We consider intuitionistic number theory with recursive infinitary rules . Any primitive recursive binary relation for which transfinite induction schema is provable is in fact well founded. Its ordinal is less than ε 0 if the transfinite induction schema is intuitionistically provable in elementary number theory. These results are provable intuitionistically. In fact, it suffices to consider transfinite induction with respect to one particular number-theoretic property

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Citations of this work

Well-foundedness in Realizability.M. Hofmann, J. van Oosten & T. Streicher - 2006 - Archive for Mathematical Logic 45 (7):795-805.

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References found in this work

A variant to Hilbert's theory of the foundations of arithmetic.G. Kreisel - 1953 - British Journal for the Philosophy of Science 4 (14):107-129.
Degrees of Unsolvability.Gerald E. Sacks - 1966 - Princeton University Press.

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