The free non-commutative cylindric algebras are not atomic

Khaled M. K. M. I.

LOGIC JOURNAL OF THE IGPL, vol.25, no.5, pp.673-685, 2017 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 25 Issue: 5
  • Publication Date: 2017
  • Doi Number: 10.1093/jigpal/jzw058
  • Journal Name: LOGIC JOURNAL OF THE IGPL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.673-685
  • Keywords: Non-permutable first-order logic, decidability, Godel's incompleteness properties, disjunctive normal forms, algebraic logic, non-commutative cylindric algebras, non-atomicity of the free algebras
  • Istanbul Medipol University Affiliated: No

Abstract

The classes of non-commutative cylindric algebras and weakened cylindric algebras were shown, by István Németi, to have decidable equational theories. In this article, we give new proof for this result and we give an answer to the open problem, posed by Németin 1985, addressing the atomicity of the finitely generated free algebras of these classes. We prove that the free algebras of these classes are not atomic.