The Barwise-Schlipf theorem
Authors:
Ali Enayat and James H. Schmerl
Journal:
Proc. Amer. Math. Soc. 149 (2021), 413-416
MSC (2010):
Primary 03C50, 03C62, 03H15
DOI:
https://doi.org/10.1090/proc/15216
Published electronically:
October 20, 2020
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Abstract | References | Similar Articles | Additional Information
Abstract: In 1975 Barwise and Schlipf published a landmark paper whose main theorem asserts that a nonstandard model of
(Peano arithmetic) is recursively saturated iff
has an expansion that satisfies the subsystem
-
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 we offer a correct proof of the problematic direction.
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- [6] C. Smoryński, Recursively saturated nonstandard models of arithmetic, J. Symbolic Logic 46 (1981), no. 2, 259–286. MR 613281, https://doi.org/10.2307/2273620
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Additional Information
Ali Enayat
Affiliation:
University of Gothenburg, Gothenburg, Sweden
Email:
ali.enayat@gu.se
James H. Schmerl
Affiliation:
University of Connecticut, Storrs, Connecticut 06269
Email:
james.schmerl@uconn.edu
DOI:
https://doi.org/10.1090/proc/15216
Received by editor(s):
November 10, 2019
Received by editor(s) in revised form:
May 24, 2020
Published electronically:
October 20, 2020
Additional Notes:
The authors are grateful to Roman Kossak, Mateusz Łełyk, and an anonymous referee for their help in improving the paper’s exposition.
Communicated by:
Heike Mildenberger
Article copyright:
© Copyright 2020
American Mathematical Society