Journal of Symbolic Logic 87 (1):416-435 (2022)

Abstract
In this paper we study a notion of HL-extension 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.
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DOI 10.1017/jsl.2020.19
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References found in this work BETA

On Extensions of Partial Isomorphisms.Mahmood Etedadialiabadi & Su Gao - 2022 - Journal of Symbolic Logic 87 (1):416-435.

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On Extensions of Partial Isomorphisms.Mahmood Etedadialiabadi & Su Gao - 2022 - Journal of Symbolic Logic 87 (1):416-435.

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