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arXiv · 1811.11120

$Λ$-ultrametric spaces and lattices of equivalence relations

Samuel Braunfeld
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Abstract

For a finite lattice $Λ$, $Λ$-ultrametric spaces have, among other reasons, appeared as a means of constructing structures with lattices of equivalence relations embedding $Λ$. This makes use of an isomorphism of categories between $Λ$-ultrametric spaces and structures equipped with certain families of equivalence relations. We extend this isomorphism to the case of infinite lattices. We also pose questions about representing a given finite lattice as the lattice of $\emptyset$-definable equivalence relations of structures with model-theoretic symmetry properties.

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Samuel Braunfeld. 2020-02-25. $Λ$-ultrametric spaces and lattices of equivalence relations. https://doi.org/10.1007/s00012-019-0606-4

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