Annals of Pure and Applied Logic 124 (1-3):193-231 (2003)

Abstract
We introduce a second-order system V1-Horn of bounded arithmetic formalizing polynomial-time reasoning, based on Grädel's 35) second-order Horn characterization of P. Our system has comprehension over P predicates , and only finitely many function symbols. Other systems of polynomial-time reasoning either allow induction on NP predicates , and hence are more powerful than our system , or use Cobham's theorem to introduce function symbols for all polynomial-time functions . We prove that our system is equivalent to QPV and Zambella's P-def. Using our techniques, we also show that V1-Horn is finitely axiomatizable, and, as a corollary, that the class of Σ1b consequences of S21 is finitely axiomatizable as well, thus answering an open question
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DOI 10.1016/s0168-0072(03)00056-3
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References found in this work BETA

Bounded Arithmetic and the Polynomial Hierarchy.Jan Krajíček, Pavel Pudlák & Gaisi Takeuti - 1991 - Annals of Pure and Applied Logic 52 (1-2):143-153.
Notes on Polynomially Bounded Arithmetic.Domenico Zambella - 1996 - Journal of Symbolic Logic 61 (3):942-966.
Relating the Bounded Arithmetic and Polynomial Time Hierarchies.Samuel R. Buss - 1995 - Annals of Pure and Applied Logic 75 (1-2):67-77.

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Citations of this work BETA

On the Finite Axiomatizability of ∀Σ̂1b.Chris Pollett - 2018 - Mathematical Logic Quarterly 64 (1-2):6-24.

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