An embedding theorem for ordered groups

The Hahn Embedding Theorem for Abelian Lattice-ordered Groups

An embedding theorem for automorphism groups of Cartan geometries

The main motivation of this paper arises from classical questions about actions of Lie groups preserving a geometric structure: which Lie groups can act on a manifold preserving a given structure, and which cannot? Which algebraic properties of the acting group have strong implications on the geometry of the manifold, such as local homogeneity, or on the dynamics of the action? These questions ...

A monotonicity theorem for dp-minimal densely ordered groups

Dp-minimality is a common generalization of weak minimality and weak o-minimality. If T is a weakly o-minimal theory then it is dp-minimal (Fact 2.2), but there are dp-minimal densely ordered groups that are not weakly o-minimal. We introduce the even more general notion of inpminimality and prove that in an inp-minimal densely ordered group, every definable unary function is a union of finitel...

A Non-quasiconvexity Embedding Theorem for Hyperbolic Groups

We show that if G is a non-elementary torsion-free word hyperbolic group then there exists another word hyperbolic group G∗, such that G is a subgroup of G∗ but G is not quasiconvex in G∗ . We also prove that any non-elementary subgroup of a torsion-free word hyperbolic group G contains a free group of rank two which is malnormal and quasiconvex in G.

An embedding theorem for Hilbert categories

We axiomatically define (pre-)Hilbert categories. The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor. We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal unit is a simple generator embeds (weakly) monoidally into the category of pre-Hilbert spaces and adjointable maps, preserving adjoint morphisms and all fini...