On Wainer's notation for a minimal subrecursive inaccessible ordinal

Mathematical Logic Quarterly 39 (1):217-227 (1993)
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Abstract

We show the following results on Wainer's notation for a minimal subrecursive inaccessible ordinal τ: First, we give a constructive proof of the collapsing theorem. Secondly, we prove that the slow-growing hierarchy and the fast-growing hierarchy up to τ have elementary properties on increase and domination, which completes Wainer's proof that τ is a minimal subrecursive inaccessible. Our results are obtained by showing a strong normalization theorem for the term structure of the notation. MSC: 03D20, 03F15

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10.1002/malq.19930390125

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Citations of this work

Accessible recursive functions.Stanley S. Wainer - 1999 - Bulletin of Symbolic Logic 5 (3):367-388.

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