TY - CHAP UR - http://lib.ugent.be/catalog/pug01:4106454 ID - pug01:4106454 LA - eng TI - A nonstandard hierarchy comparison theorem for the slow and fast growing hierarchy PY - 2012 SN - 9783868381580 PB - Frankfurt AU - Buchholz, Wilfried AU - Weiermann, Andreas WE01 802000038735 0000-0002-5561-5323 AU - Berger, Ulrich editor AU - Diener, Hannes editor AU - Schuster, Peter editor AU - Seisenberger, Monika editor AB - It is folklore that the slow and fast growing hierarchy match up for the first time at the proof-theoretic ordinal of (Pi^1_1-CA)_0. By results of Schütte and Simpson it is known that the underlying notation system looses its strengths when the ordinal addition function is no longer present. In this article we will show that a hierarchy comparison can still be established. Surprisingly the match of the slow and fast growing hierarchy can be arranged by using standard fundamental sequences to happen at omega^2 which is much smaller than the ordinal of (Pi^1_1-CA)_0.We will also show that the slow growing hierarchy consists of elementary functions only when it is based on a Buchholz style system of fundamental sequences for the Schütte Simpson ordinal notations system. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 4106454 | ||
005 | 20180813142855.0 | ||
008 | 130723s2012------------------------eng-- | ||
020 | a 9783868381580 | ||
024 | a 1854/LU-4106454 2 handle | ||
040 | a UGent | ||
245 | a A nonstandard hierarchy comparison theorem for the slow and fast growing hierarchy | ||
260 | a Frankfurt, Germany b Ontos c 2012 | ||
520 | a It is folklore that the slow and fast growing hierarchy match up for the first time at the proof-theoretic ordinal of (Pi^1_1-CA)_0. By results of Schütte and Simpson it is known that the underlying notation system looses its strengths when the ordinal addition function is no longer present. In this article we will show that a hierarchy comparison can still be established. Surprisingly the match of the slow and fast growing hierarchy can be arranged by using standard fundamental sequences to happen at omega^2 which is much smaller than the ordinal of (Pi^1_1-CA)_0.We will also show that the slow growing hierarchy consists of elementary functions only when it is based on a Buchholz style system of fundamental sequences for the Schütte Simpson ordinal notations system. | ||
598 | a B2 | ||
100 | a Buchholz, Wilfried | ||
700 | a Weiermann, Andreas u WE01 0 802000038735 0 0000-0002-5561-5323 | ||
700 | a Berger, Ulrich e editor | ||
700 | a Diener, Hannes e editor | ||
700 | a Schuster, Peter e editor | ||
700 | a Seisenberger, Monika e editor | ||
650 | a Mathematics and Statistics | ||
653 | a ordinal notation systems | ||
653 | a slow growing hierarchy | ||
653 | a subrecursive hierarchies | ||
653 | a proof theory | ||
653 | a fast growing hierarchy | ||
773 | t Logic, construction, computation g Logic, construction, computation. 2012. Ontos. 3 p.79-90 q 3:<79 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/4106454/file/4106455 z [ugent] y buchholzweiermannslowfast.pdf | ||
920 | a chapter | ||
Z30 | x WE 1 WE01 | ||
922 | a UGENT-WE |
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