Blowing up and blurring finite Monk and rainbow algebras

2013/05/20 by Tarek Sayed Ahmed, Ahmed, Tarek Sayed · 3 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebraic structures and combinatorial models #FOS: Mathematics #Logic (math.LO) #Logic, programming, and type systems #math.LO

paper · pdf · doi:10.48550/arxiv.1305.4570

arxiv created 2013/05/20 · openalex publication_date 2013/05/20 · arxiv updated 2013/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use Monk like algebras to give a new proof that the classes of strongly representable relation algebras and finite dimensional cylindric algebras of dimension >2 are not elementary. Our construction is based on relation algebras have cylindric basis, so that we obtain the result for both in one go, since they are both based on the same graph. The proof also uses Erdos' graphs. We also show using a rainbow construction that the class SNr_n\CA_n+k is not atom canonical, for any k≥ 4.

Cited by

• 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
• On completions, neat embeddings and omittings types, yet again
• Strongly representable atom structures and neat embeddings

Related

• Various interplays between relation and cylindric algebras
• Strongly representable atom structures and neat embeddings
• Strongly representable atom structures
• Strongly representable algebras
• Dedekind completions, neat embeddings and omitting types