First order logic without equality on relativized semantics


Banerjee A., Khaled M. K. M. I.

Annals of Pure and Applied Logic, vol.169, no.11, pp.1227-1242, 2018 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 169 Issue: 11
  • Publication Date: 2018
  • Doi Number: 10.1016/j.apal.2018.07.002
  • Journal Name: Annals of Pure and Applied Logic
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1227-1242
  • Keywords: Atoms, Free algebras, Zero-dimensional elements
  • Istanbul Medipol University Affiliated: No

Abstract

Let α≥2 be any ordinal. We consider the class Drsα of relativized diagonal free set algebras of dimension α. With same technique, we prove several important results concerning this class. Among these results, we prove that almost all free algebras of Drsα are atomless, and none of these free algebras contains zero-dimensional elements other than zero and top element. The class Drsα corresponds to first order logic, without equality symbol, with α-many variables and on relativized semantics. Hence, in this variation of first order logic, there is no finitely axiomatizable, complete and consistent theory.