Beziehungen des Ordinalzahlensystems OT(ϑ) zur Veblen-Hierarchie

Kurt Schütte ()
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Kurt Schütte: Mathematisches Institut

Chapter Chapter 23 in The Legacy of Kurt Schütte, 2020, pp 461-469 from Springer

Abstract: Abstract This paper of Schutte’s is from 1992. In it Schutte compares two ordinal representation systems, namely, OT(ϑ) from [2] which was utilized by Rathjen and Weiermann in [3] in their proof-theoretic investigations of Kruskal’s theorem, and the Veblen hierarchy as presented via Schutte’s Klammersymbole in [4]. Schutte then uses this comparison to locate several signature ordinals within OT(ϑ), e.g., Γ0, Ackermann’s ordinal from [1], the small Veblen number, and the big Veblen number. For the proof of the crucial technical Lemma 23.4.2, however, Schutte provides only a hint. As discussions between Wilfried Buchholz and Michael Rathjen could not exactly clarify which proof Schutte had envisaged, it was felt that it was a good idea to supply a more complete one. Thankfully,Wilfried Buchholz devised and wrote up such a proof which is now incorporated in the paper. Of course, we cannot ascertain that this is what Schutte had in mind.

Date: 2020
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DOI: 10.1007/978-3-030-49424-7_23

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