2014/07/31 by Brett McLean · 7 citations
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebra over a field #Class (philosophy) #Composition (language) #Computer science #Discrete mathematics #Domain (mathematical analysis) #Intersection (aeronautics) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems #Mathematics #Partial function #Pure mathematics #Representation (politics) #Representation theorem #Signature (topology) #math.LO #math.RA
paper · pdf · doi:10.1093/logcom/exu081
published in Journal of Logic and Computation 27(4), 1143-1156 (Oxford University Press) · 14 pages. Additional non-axiomatisability results added
arxiv created 2014/11/20 · openalex publication_date 2015/01/30 · arxiv updated 2017/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
For representation by partial functions in the signature with intersection, composition and anti-domain, we show that a representation is meet complete if and only if it is join complete. We show that a representation is complete if and only if it is atomic, but that not all atomic representable algebras are completely representable. We show that the class of completely representable algebras is not axiomatizable by any existential-universal-existential first-order theory. By giving an explicit representation, we show that the completely representable algebras form a basic elementary class, axiomatizable by a universal-existential-universal sentence.