Year: 2026
Type: preprint
Abstract: A hard theorem of Givant classifies the finitary algebraic theories for which every algebra is free. From it, one easily deduces that all such theories are minimal (adding any further equations makes them trivial) and have a well-defined notion of dimension (free algebras on sets of different cardinality are never isomorphic). We prove both these properties directly, without the aid of Givant's theorem.
Source: arXiv (Cornell University)
Authors: Leinster, Tom, Woolf, Maia
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: University and College Union
OpenAlex ID: W7223261194