Research Training Network in Model Theory
Publications > Preprint server > Preprint Number 714

Preprint Number 714

Previous Next Preprint server

714. Kaisa Kangas
Finding groups in Zariski-like structures

Submission date: 27 April 2014.


We study quasiminimal classes, i.e. abstract elementary classes (AECs) that arise from a quasiminimal pregeometry structure. For these classes, we develop an independence notion, and in particular, a theory of independence in M^{eq}. We then generalize Hrushovski's Group Configuration Theorem to our setting. In an attempt to generalize Zariski geometries to the context of quasiminimal classes, we give the axiomatization for Zariski-like structures, and as an application of our group configuration theorem, show that groups can be found in them assuming that the pregeometry obtained from the bounded closure operator is non-trivial. Finally, we study the cover of the multiplicative group of an algebraically closed field and show that it provides an example of a Zariski-like structure.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 1404.6811: pdf, ps.

Last updated: March 23 2021 10:22 Please send your corrections to: