Incompleteness of boundedly axiomatizable theories
Logic
2024-02-19 v4
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+).
Keywords
Cite
@article{arxiv.2311.14025,
title = {Incompleteness of boundedly axiomatizable theories},
author = {Ali Enayat and Albert Visser},
journal= {arXiv preprint arXiv:2311.14025},
year = {2024}
}
Comments
6 pages; in this version reference to MathOverflow work of Emil Je\v{r}\'{a}bek has been added, and the author list of [AGLRZ] is now up-to-date