The free non-commutative cylindric algebras are not atomic

Creative Commons License

Khaled M. K. M. I.

Logic Journal of the IGPL, cilt.25, sa.5, ss.673-685, 2017 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 25 Sayı: 5
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1093/jigpal/jzw058
  • Dergi Adı: Logic Journal of the IGPL
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.673-685
  • Anahtar Kelimeler: Algebraic logic, Decidability, Disjunctive normal forms, Gödel's incompleteness properties, Non-atomicity of the free algebras, Non-commutative cylindric algebras, Non-permutable first-order logic
  • İstanbul Medipol Üniversitesi Adresli: Hayır

Özet

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.