Year: 2026
Type: article
Abstract: A structure is ultrahomogeneous if every isomorphism between finitely generated substructures can be extended to an automorphism of the structure. The aim of this paper is to provide an explicit description of ultrahomogeneous monounary algebras of arbitrary cardinalities. We also show that a monounary algebra is ultrahomogeneous if and only if it is 1-ultrahomogeneous. These results are then viewed in the context of a several related concepts, including ω -categoricity, homomorphism-homogeneity, (partial-)homogeneity, and transitivity.
Source: Mathematica Slovaca
DOI: 10.1515/ms-2026-0222
Author: Thomas Quinn-Gregson
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Award: G3198978689
OpenAlex ID: W7143542099