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Interpreting Weak König's Lemma using the Arithmetized Completeness Theorem


Author: Tin Lok Wong
Journal: Proc. Amer. Math. Soc. 144 (2016), 4021-4024
MSC (2010): Primary 03C62, 03F25, 03H15
DOI: https://doi.org/10.1090/proc/13125
Published electronically: April 20, 2016
MathSciNet review: 3513557
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Abstract: We present a previously unpublished proof of the conservativity of $ \mathrm {WKL}_0$ over  $ \mathrm I\Sigma _1$ using the Arithmetized Completeness Theorem, which, in particular, constitutes an $ \omega $-interpretation of  $ \mathrm {WKL}_0$ in  $ \mathrm I\Sigma _1$. We also show that $ \mathrm {WKL}_0^*$ is interpretable in $ \mathrm I\Delta _0+\mathrm {exp}$.


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Additional Information

Tin Lok Wong
Affiliation: Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Austria
Email: tin.lok.wong@univie.ac.at

DOI: https://doi.org/10.1090/proc/13125
Received by editor(s): July 10, 2015
Received by editor(s) in revised form: October 2, 2015, and November 6, 2015
Published electronically: April 20, 2016
Additional Notes: Part of this paper was presented at the Logic Colloquium in Vienna, Austria, in July 2014. The author was financially supported by the Austrian Science Fund (FWF) project P24654-N25 while this research was carried out.
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2016 American Mathematical Society