We consider Peterzil-Steinhorn groups defined in o-minimal expansions of the reals. These are one-dimensional torsion-free subgroups of arbitrary definable and not definably compact groups. We show that each Peterzil-Steinhorn group is isomorphic to either the additive or the multiplicative group of the reals and we provide a simple criterion that can be used to classify each such group into one of those two categories. Additionally, we find the tangent space of any arbitrary Peterzil-Steinhorn group at its identity. Finally, for the case of polynomially bounded o-minimal expansions of the reals, we give a complete description of all Peterzil-Steinhorn groups.
|Contributor||Liviu Nicolaescu, Committee Member|
|Contributor||Vincent Guingona, Committee Member|
|Contributor||Anand Pillay, Committee Member|
|Contributor||Sergei Starchenko, Committee Chair|
|Degree Level||Doctoral Dissertation|
|Departments and Units|