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Ordinal notations and well-orderings in bounded arithmetic

✍ Scribed by Arnold Beckmann; Chris Pollett; Samuel R. Buss


Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
244 KB
Volume
120
Category
Article
ISSN
0168-0072

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πŸ“œ SIMILAR VOLUMES


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## Abstract The class of all ordinal numbers can be partitioned into two subclasses in such a way that neither subclass contains an arithmetic progression of order type Ο‰, where an arithmetic progression of order type Ο„ means an increasing sequence of ordinal numbers (ß + δγ)Ξ³<Ξ³<>r, Ξ΄ β‰  0.

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We study search problems and reducibilities between them with known or potential relevance to bounded arithmetic theories. Our primary objective is to understand the sets of low complexity consequences (esp. Ξ£ b 1 or Ξ£ b 2 ) of theories S i 2 and T i 2 for a small i, ideally in a rather strong sense

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The bounded arithmetic theories R i 2 ; S i 2 , and T i 2 are closely connected with complexity theory. This paper is motivated by the questions: what are the b i+1 -deΓΏnable multifunctions of R i 2 ? and when is one theory conservative over another? To answer these questions we consider theories Ri