Incompleteness of boundedly axiomatizable theories
- 20 September 2024
- journal article
- research article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 152 (11) , 4923-4932
Abstract
Our main result (Theorem A) shows the incompleteness of any consistent sequential theory T T formulated in a finite language such that T T is axiomatized by a collection of sentences of bounded quantifier-alternation-depth. Our proof employs an appropriate reduction mechanism to rule out the possibility of completeness by simply invoking Tarski’s Undefinability of Truth theorem. We also use the proof strategy of Theorem A to obtain other incompleteness results.Keywords
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Funding Information
- Narodowe Centrum Nauki (2019/34/A/HS1/00399)
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