On Wainer's notation for a minimal subrecursive inaccessible ordinal

✍ Scribed by Noriya Kadota

• Book ID: 102941881
• Publisher: John Wiley and Sons
• Year: 1993
• Tongue: English
• Weight: 533 KB
• Volume: 39
• Category: Article
• ISSN: 0044-3050
• DOI: 10.1002/malq.19930390125

✦ Synopsis

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.