Abstract

It is well-known that IΣ1 is ΙΙ2-conservative over PRA. This fact
is often referred to as Parsons’ theorem. In this paper we provide two
proofs of the theorem. One is proof-theoretic and easily formalizable.
The other proof is model-theoretic. The main ingredient of the second
proof is a characterization of IΣ1 in terms of
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