caa a22 4500 388039795 CHVBK 20180307125018.0 cr unu---uuuuu 161130e199809 xx s 000 0 eng 10.2307/2586719 doi S0022481200014663 pii (NATIONALLICENCE)cambridge-10.2307/2586719 Arai Toshiyasu Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan E-mail: arai@mis.hiroshima-u.ac.jp Variations on a theme by Weiermann [Elektronische Daten] [Toshiyasu Arai] Weiermann [18] introduces a new method to generate fast growing functions in order to get an elegant and perspicuous proof of a bounding theorem for provably total recursive functions in a formal theory, e.g., in PA. His fast growing function θαη is described as follows. For each ordinal a and natural number n let denote a finitely branching, primitive recursive tree of ordinals, i.e., an ordinal as a label is attached to each node in the tree so that the labelling is compatible with the tree ordering. Then the tree is well founded and hence finite by König's lemma. Define θαηn =the depth of the tree =the length of the longest branch in . We introduce new fast and slow growing functions in this mode of definitions and show that each of these majorizes provably total recursive functions in PA. Copyright © Association for Symbolic Logic 1998 The Journal of Symbolic Logic Cambridge University Press 63/3(1998-09), 897-925 0022-4812 63:3<897 1998 63 JSL https://doi.org/10.2307/2586719 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586719 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Arai Toshiyasu Faculty of Integrated Arts and Sciences, Hiroshima University, Higashi-Hiroshima, 739-8521, Japan E-mail: arai@mis.hiroshima-u.ac.jp NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/3(1998-09), 897-925 0022-4812 63:3<897 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge