Year: 2020
Type: article
Abstract: In this paper we study a notion of HL-extension (HL standing for Herwig–Lascar) for a structure in a finite relational language $\mathcal {L}$ . We give a description of all finite minimal HL-extensions of a given finite $\mathcal {L}$ -structure. In addition, we study a group-theoretic property considered by Herwig–Lascar and show that it is closed under taking free products. We also introduce notions of coherent extensions and ultraextensive $\mathcal {L}$ -structures and show that every countable $\mathcal {L}$ -structure can be extended to a countable ultraextensive structure. Finally, it follows from our results that the automorphism group of any countable ultraextensive $\mathcal {L}$ -structure has a dense locally finite subgroup.
Source: Journal of Symbolic Logic
DOI: 10.1017/jsl.2020.19
Authors: MAHMOOD ETEDADIALIABADI, SU GAO
Institution: University of North Texas
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2965593088