A note on the Π 0 2 – induction rule ∗
نویسنده
چکیده
It is well–known (due to C. Parsons) that the extension of primitive recursive arithmetic PRA by first–order predicate logic and the rule of Π02–induction Π02–IR is Π 0 2–conservative over PRA. We show that this is no longer true in the presence of function quantifiers and quantifier–free choice for numbers AC– qf. More precisely we show that T :=PRA + Π02–IR+AC –qf proves the totality of the Ackermann function, where PRA is the extension of PRA by number and function quantifiers and Π02–IR may contain function parameters. This is true even for PRA +Σ01–IR+Π 0 2–IR +AC–qf, where Π02–IR − is the restriction of Π02–IR without function parameters.
منابع مشابه
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