The free non-commutative cylindric algebras are not atomic
LOGIC JOURNAL OF THE IGPL, cilt.25, sa.5, ss.673-685, 2017 (SCI-Expanded, Scopus)
- 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: 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
- 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.