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Levelled O-minimal structures.

David Marker, Chris Miller (1997)

Revista Matemática de la Universidad Complutense de Madrid

We introduce the notion of leveled structure and show that every structure elementarily equivalent to the real expo field expanded by all restricted analytic functions is leveled.

Limits of relatively hyperbolic groups and Lyndon’s completions

Olga Kharlampovich, Alexei Myasnikov (2012)

Journal of the European Mathematical Society

We describe finitely generated groups H universally equivalent (with constants from G in the language) to a given torsion-free relatively hyperbolic group G with free abelian parabolics. It turns out that, as in the free group case, the group H embeds into the Lyndon’s completion G [ t ] of the group G , or, equivalently, H embeds into a group obtained from G by finitely many extensions of centralizers. Conversely, every subgroup of G [ t ] containing G is universally equivalent to G . Since finitely generated...

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