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The predicative Frege hierarchy

By A. Visser


In this paper, we characterize the strength of the predicative Frege hierarchy,\ud Pn+1V, introduced by John Burgess in his book [Burg05]. We show\ud that Pn+1V and Q + conn(Q) are mutually interpretable. It follows that\ud PV := P1V is mutually interpretable with Q. This fact was proved earlier\ud by Mihai Ganea in [Gan06] using a different proof. Another consequence\ud of the our main result is that P2V is mutually interpretable with Kalmar\ud Arithmetic (a.k.a. EA, EFA, IΔ0+EXP, Q3). The fact that P2V interprets\ud EA, was proved earlier by Burgess. We provide a different proof.\ud Each of the theories Pn+1V is finitely axiomatizable. Our main result\ud implies that the whole hierarchy taken together, PωV, is not finitely\ud axiomatizable. What is more: no theory that is mutually locally interpretable\ud with PωV is finitely axiomatizable

Topics: Wijsbegeerte, predicative comprehension, Frege, interpretability
Year: 2006
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