arXiv subjects

Pantelis Eleftheriou

Publications and source records attributed to Pantelis Eleftheriou.

5 recordsLinked to original sources

arXiv2021

Strongly minimal groups in o-minimal structures

We prove Zilber's Trichotomy Conjecture for strongly minimal expansions of two-dimensional groups, definable in o-minimal structures: Theorem. Let M be an o-minimal expansion of a real closed field, (G;+) a 2-dimensional group definable in M, and D = (G;+,...) a strongly minimal structure, all of whose atomic relations are definable in M. If D is not locally modular, then an algebraically closed field K is interpretable in D, and the group G, with all its induced D-structure, is definably isomorphic in D to an algebraic K-group with all its induced K-structure.

math.LO↗

arXiv2014

Coverings by open cells

We prove that in a semi-bounded o-minimal expansion of an ordered group every non-empty open definable set is a finite union of open cells.

math.LO↗

arXiv2012

Definable quotients of locally definable groups

We study locally definable abelian groups $\CU$ in various settings and examine conditions under which the quotient of $\CU$ by a discrete subgroup might be definable. This turns out to be related to the existence of the type-definable subgroup $\CU^{00}$ and to the divisibility of $\CU$.

math.LO↗

arXiv2012

Definable groups as homomorphic images of semilinear and field-definable groups

We analyze definably compact groups in o-minimal expansions of ordered groups as a combination of semi-linear groups and groups definable in o-minimal expansions of real closed fields. The analysis involves structure theorems about their locally definable covers. As a corollary, we prove the Compact Domination Conjecture in o-minimal expansions of ordered groups.

math.LO↗

arXiv2011

Interpretable groups are definable

We prove that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. We also prove that every definable group lives in a cartesian product of one-dimensional definable group-intervals (or one-dimensional definable groups). We discuss the general open question of elimination of imaginaries in an o-minimal structure.

math.LO↗