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A bounded arithmetic AID for Frege systems

✍ Scribed by Toshiyasu Arai

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
303 KB
Volume
103
Category
Article
ISSN
0168-0072

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✦ Synopsis

In this paper we introduce a system AID (alogtime inductive deΓΏnitions) of bounded arithmetic. The main feature of AID is to allow a form of inductive deΓΏnitions, which was extracted from Buss' propositional consistency proof of Frege systems F in Buss (Ann. Pure Appl. Logic 52 (1991) 3-29). We show that AID proves the soundness of F, and conversely any b 0 -theorem in AID yields boolean sentences of which F has polysize proofs. Further we deΓΏne b 1 -faithful interpretations between AID + b 0 -CA and a quantiΓΏed theory QALV of an equational system ALV in Clote (Ann. Math. Art. Intell. 6 (1992) 57-106). Hence ALV also proves the soundness of F.

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