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.
Original language | English |
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Pages (from-to) | 2513-2531 |
Number of pages | 19 |
Journal | Bulletin of the London Mathematical Society |
Volume | 54 |
Issue number | 6 |
DOIs | |
Publication status | Published - Dec 2022 |
Bibliographical note
Publisher Copyright:© 2022 The Authors. The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.