Incompleteness of boundedly axiomatizable theories

Ali Enayat, Albert Visser

Research output: Working paperPreprintAcademic

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+).
Original languageEnglish
PublisherarXiv
Number of pages6
DOIs
Publication statusPublished - 23 Nov 2023

Keywords

  • math.LO
  • 03F40

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