2013/04/04 by Tarek Sayed Ahmed, Ahmed, Tarek Sayed
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Rings, Modules, and Algebras #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1304.1429
openalex publication_date 2013/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Usually when we have polyadic-like algebras, meaning that we have infinitary substitutions (that is substitutions moving infinitely many points) in the similarity type, then we get the superamalgamation property especially if this class of algebras happen to be a variety. This for example happens for (full) polyadic algebras, full Heyting algebras and reducts of those using only finitely many infinitary substitutions, like Sains Boolean and Heyting algebras. (The last is studied by Sayed Ahmed) . In cylindric-like algebras (like quasi-polyadic algebras) when we do not have infinitary substitutions, we do not get even the amalgamation property . In this paper, we give an example of a polyadic like variety (we have infinitary substitutions, in fact infinitely many of them) for which the amalgamation property fails.