Incompleteness of boundedly axiomatizable theories

Ali Enayat; Albert Visser

doi:10.1090/proc/16975

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arXiv · 2311.14025

Incompleteness of boundedly axiomatizable theories

Ali Enayat·Albert Visser

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Abstract

Our main result (Theorem A) shows the incompleteness of any consistent sequential theory T formulated in a finite language such that 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 (as in Theorems A+; B and B+).

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BibTeX RIS

Ali Enayat, Albert Visser. 2023-11-23. Incompleteness of boundedly axiomatizable theories. https://doi.org/10.1090/proc%2F16975

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