Unprovability of Consistency Statements in Fragments of Bounded Arithmetic (1995)
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by
Samuel R. Buss
,
Aleksandar Ignjatovic
| Citations: | 4 - 2 self |
BibTeX
@MISC{Buss95unprovabilityof,
author = {Samuel R. Buss and Aleksandar Ignjatovic},
title = {Unprovability of Consistency Statements in Fragments of Bounded Arithmetic},
year = {1995}
}
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Abstract
This paper deals with the weak fragments of arithmetic PV and S and their induction-free fragments PV - and S -1 2 . We improve the bootstrapping of S 2 , which allows us to show that the theory S 2 can be axiomatized by the set of axioms BASIC together with any of the following induction schemas: # 1 -PIND , # 1 -PIND or # 1 -LIND .
Citations
| 110 | Feasibly constructive proofs and the propositional calculus - Cook - 1975 |
| 18 | conservation results for fragments of bounded arithmetic, in Logic and Computation, proceedings of a Workshop held Carnegie-Mellon - Axiomatizations - 1987 |
| 3 | Some relations among systems for bounded arithmetic - Takeuti - 1990 |
| 2 | c, Delineating classes of computational complexity via second order theories with weak set existence principles (I - Ignjatovi - 1991 |
| 1 | Letter to P - Buss - 1986 |
| 1 | ak, A note on bounded arithmetic - Pudl - 1990 |
