Complete representation by partial functions for composition, intersection and antidomain

Abstract

For representation by partial functions in the signature with intersection, composition and antidomain, 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 axiomatisable 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, axiomatisable by a universal-existential-universal sentence.

14 pages. Additional non-axiomatisability results added

References in corpus (1)

• Completely Representable Lattices

Cited by in corpus (4)

• Difference-restriction algebras of partial functions: axiomatisations and representations
• Disjoint-union partial algebras
• Difference-restriction algebras of partial functions with operators: discrete duality and completion
• Complete representation by partial functions for signatures containing antidomain restriction