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  1. Stably embedded submodels of Henselian valued fields.Pierre Touchard - 2023 - Archive for Mathematical Logic 63 (3):279-315.
    We show a transfer principle for the property that all types realised in a given elementary extension are definable. It can be written as follows: a Henselian valued field is stably embedded in an elementary extension if and only if its value group is stably embedded in its corresponding extension, its residue field is stably embedded in its corresponding extension, and the extension of valued fields satisfies a certain algebraic condition. We show for instance that all types over the Hahn (...)
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  • Discrete Sets Definable in Strong Expansions of Ordered Abelian Groups.Alfred Dolich & John Goodrick - forthcoming - Journal of Symbolic Logic:1-37.
    We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with a particular emphasis on the set $D'$ comprised of differences between successive elements. In particular, if the burden of the structure is at most n, then the result of applying the operation $D \mapsto D'\ n$ times must be a finite set (Theorem 1.1). In the case when the structure is densely ordered and has burden $2$, (...)
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