# A Complete Finite Axiomatisation of the Equational Theory of Common Meadows

arXiv: https://arxiv.org/abs/2307.04270 · HTML: https://mlsanity.com/paper/2307.04270/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2023.

## Built on by (most cited first, 1 of 1)

- [On Ambiguity: The case of fraction, its meanings and roles](https://mlsanity.com/paper/2604.04647/) (2026)

## Abstract (arXiv)

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 bot whose main purpose is to always return a value for division. To rings and fields, we add a division operator x/y and study a class of algebras called common meadows wherein x/0 = bot. The set of equations true in all common meadows is named the equational theory of common meadows. We give a finite equational axiomatisation of the equational theory of common meadows and prove that it is complete and that the equational theory is decidable.