The Barwise-Schlipf Theorem

2019/11/12 by Ali Enayat, Enayat, Ali, James H. Schmerl +1
Mathematics · #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1911.05117

Abstract

In 1975 Barwise and Schlipf published a landmark paper whose main theorem asserts that a nonstandard model M of PA (Peano arithmetic) is recursively saturated iff M has an expansion that satisfies the subsystem Δ₁¹-\sf CA₀ of second order arithmetic. In this paper we identify a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, and additionally, we offer a correct proof of the problematic direction.

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