Premium
Γ 0 May Be Minimal Subrecursively Inaccessible
Author(s) -
Weiermann Andreas
Publication year - 2001
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/1521-3870(200108)47:3<397::aid-malq397>3.0.co;2-y
Subject(s) - predicative expression , mathematics , hierarchy , limit (mathematics) , discrete mathematics , pure mathematics , linguistics , philosophy , mathematical analysis , law , political science
Let T be the standard Veblen 1908 ordinal notation system for Γ 0 as defined, for example, in Schütte's 1977 textbook [13] on Proof Theory. We define a slight modification of the standard assignment of fundamental sequences for the limit ordinals in T and prove that Γ 0 is subrecursively inaccessible for this assignment, i.e. the induced slow and fast growing hierarchy match up at Γ 0 for the first time.The results of this paper also indicate that φε 0 0 may be considered as a new slow growing ordinal of PA in the sense that the induced slow growing hierarchy up to φε 0 0 classifies the PA‐provablyrecursive functions.We show how the results of this paper can be used to bui d a subrecursive hierarchyover the predicative ordinals in the spirit of Wainer's 1970 abstract [16 ].