The Witness Function Method and Provably Recursive Functions of Peano Arithmetic
نویسنده
چکیده
This paper presents a new proof of the characterization of the provably recursive functions of the fragments IΣn of Peano arithmetic. The proof method also characterizes the Σk -definable functions of IΣn and of theories axiomatized by transfinite induction on ordinals. The proofs are completely proof-theoretic and use the method of witness functions and witness oracles. Similar methods also yield a new proof of Parson’s theorem on the conservativity of the Σn+1 -induction rule over the Σn -induction axioms. A new proof of the conservativity of BΣn+1 over IΣn is given. The proof methods provide new analogies between Peano arithmetic and bounded arithmetic.
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