2023/11/23 by Enayat, Ali, Visser, Albert · 1 citation
#03F40 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2311.14025
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+).