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arXiv · 1911.05117

The Barwise-Schlipf Theorem

Ali Enayat·James H. Schmerl
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Abstract

In 1975 Barwise and Schlipf published a landmark paper whose main theorem asserts that a nonstandard model $\mathcal{M}$ of PA (Peano arithmetic) is recursively saturated iff $\mathcal{M}$ has an expansion that satisfies the subsystem $\Delta_1^1$-${\sf CA}_0$ 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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Ali Enayat, James H. Schmerl. 2019-11-12. The Barwise-Schlipf Theorem. https://arxiv.org/abs/1911.05117

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