A Complete Finite Axiomatisation of the Equational Theory of Common Meadows - John Tucker (ACM Transactions on Computational Logic, 2025)
We analyse abstract data types that model numerical structures with a concept of error. Specifically, we focus on arithmetic data types that contain an error value whose main purpose is to alwaysreturn a value for division. To rings and fields, we add a division operatorx/y and study a class of algebras called common meadows whereinx/0 is the error value. The set of equations true in all common meadows is namedthe equational theory of common meadows. We give a finite equationalaxiomatisation of the equational theory of common meadows and provethat it is complete and that the equational theory is decidable.