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  1. Dynamic Ordinal Analysis.Arnold Beckmann - 2003 - Archive for Mathematical Logic 42 (4):303-334.
    Dynamic ordinal analysis is ordinal analysis for weak arithmetics like fragments of bounded arithmetic. In this paper we will define dynamic ordinals – they will be sets of number theoretic functions measuring the amount of sΠ b 1(X) order induction available in a theory. We will compare order induction to successor induction over weak theories. We will compute dynamic ordinals of the bounded arithmetic theories sΣ b n (X)−L m IND for m=n and m=n+1, n≥0. Different dynamic ordinals lead to (...)
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  • A Note on Conservativity Relations Among Bounded Arithmetic Theories.Russell Impagliazzo & Jan Krajíček - 2002 - Mathematical Logic Quarterly 48 (3):375-377.
    For all i ≥ 1, Ti+11 is not ∀Σb2-conservative over Ti1.
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  • Structure and Definability in General Bounded Arithmetic Theories.Chris Pollett - 1999 - Annals of Pure and Applied Logic 100 (1-3):189-245.
    The bounded arithmetic theories R2i, S2i, and T2i are closely connected with complexity theory. This paper is motivated by the questions: what are the Σi+1b-definable multifunctions of R2i? and when is one theory conservative over another? To answer these questions we consider theories , and where induction is restricted to prenex formulas. We also define which has induction up to the 0 or 1-ary L2-terms in the set τ. We show and and for . We show that the -multifunctions of (...)
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  • Witnessing Functions in Bounded Arithmetic and Search Problems.Mario Chiari & Jan Krajíček - 1998 - Journal of Symbolic Logic 63 (3):1095-1115.
    We investigate the possibility to characterize (multi) functions that are Σ b i -definable with small i (i = 1, 2, 3) in fragments of bounded arithmetic T 2 in terms of natural search problems defined over polynomial-time structures. We obtain the following results: (1) A reformulation of known characterizations of (multi)functions that are Σ b 1 - and Σ b 2 -definable in the theories S 1 2 and T 1 2 . (2) New characterizations of (multi)functions that are (...)
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