Neat atom structures

2013/04/02 by Tarek Sayed Ahmed, Ahmed, Tarek Sayed · 4 citations
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Logic (math.LO) #Rings, Modules, and Algebras #math.LO

paper · pdf · doi:10.48550/arxiv.1304.0785

arXiv admin note: text overlap with arXiv:1302.1368

arxiv created 2013/04/02 · openalex publication_date 2013/04/02 · arxiv updated 2013/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An atom structure is neat if there an algebra based on this atom structure in Nr_nCA_ω. We show that this class is not elementary

Citations

• On the finitizability problem in algebraic logic; recent results

Cited by

• On some open problems in Algebraic logic
• The elementary closure of the class Nr_nCA_m for m≥ n+1 is not finitely axiomatizable, futhermore for any finite k≥ 1, there is A∈ Nr_ωCA_\omeg+kthat is not SNr_ωCA_ω+k+1
• Various interplays between relation and cylindric algebras
• For finite n≥ 3, and k≥ 4, the variety SNr_n\CA_n+k is not atom canonical

Related

• On neat atom structures for cylindric like algebras
• Strongly representable atom structures and neat embeddings
• Strongly representable atom structures
• Blowing up and blurring finite Monk and rainbow algebras
• Various interplays between relation and cylindric algebras