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Finitely axiomatized theories lack self‐comprehension

Finitely axiomatized theories lack self‐comprehension In this paper, we prove that no consistent finitely axiomatized theory one‐dimensionally interprets its own extension with predicative comprehension. This constitutes a result with the flavor of the Second Incompleteness Theorem whose formulation is completely arithmetic‐free. Probably the most important novel feature that distinguishes our result from the previous results of this kind is that it is applicable to arbitrary weak theories, rather than to extensions of some base theory. The methods used in the proof of the main result yield a new perspective on the notion of sequential theory, in the setting of forcing‐interpretations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

Finitely axiomatized theories lack self‐comprehension

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References (22)

Publisher
Wiley
Copyright
© 2022 London Mathematical Society.
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms.12708
Publisher site
See Article on Publisher Site

Abstract

In this paper, we prove that no consistent finitely axiomatized theory one‐dimensionally interprets its own extension with predicative comprehension. This constitutes a result with the flavor of the Second Incompleteness Theorem whose formulation is completely arithmetic‐free. Probably the most important novel feature that distinguishes our result from the previous results of this kind is that it is applicable to arbitrary weak theories, rather than to extensions of some base theory. The methods used in the proof of the main result yield a new perspective on the notion of sequential theory, in the setting of forcing‐interpretations.

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Dec 1, 2022

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