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

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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DOI 10.1016/0168-0072(86)90004-7
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References found in this work BETA

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 - 1963 - Princeton University Press.

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

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