2013/06/04 by Tarek Sayed Ahmed, Ahmed, Tarek Sayed
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #math.LO
paper · pdf · doi:10.48550/arxiv.1306.1464
Submitted to the Journal of Symbolic Logic. arXiv admin note: substantial text overlap with arXiv:1301.5850
arxiv created 2013/06/04 · openalex publication_date 2013/06/04 · arxiv updated 2013/06/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
We prove the result in the title. We infer, that unlike cylindric algebras, there is a first order axiomatization of the class of completely representable polyadic algebras of infinite dimension, though the one we obtain is infinite; in fact uncountable, but shares a single schema, stipulating that the (uncountably many)substitution operators are completely additive. Similar results are obtained for non commutative reducts of polyadic equality algebras of infinite dimensions, where we can drop complete additivity. However, it remains unknown to us whether there are atomic polyadic algebras of infinite dimension that are not completely additive; but we strongly conjecture that there are.