Pantelis E. Eleftheriou

The universal covering homomorphism in o‐minimal expansions of groups

FCT (Fundacao para a Ciencia e Tecnologia), program POCTI (Portugal/FEDER-EU); NSF grant DMS-02-45167 (Cholak)

Notions of Bisimulation for Heyting-Valued Modal Languages

We examine the notion of bisimulation and its ramifications, in the context of the family of Heyting-valued modal languages introduced by M. Fitting. Each modal language in this family is built on an underlying space of truth values, a Heyting algebra H. All the truth values are directly represented in the language, which is interpreted on relational frames with an H-valued accessibility relation. We define two notions of bisimulation that allow us to obtain truth invariance results. We provide game semantics and, for the more interesting and complicated notion, we are able to provide characteristic formulae and prove a Hennessy–Milner-type theorem. If the underlying algebra H is finite, Heyting-valued modal models can be equivalently reformulated to a form relevant to epistemic situations with many interrelated experts. Our definitions and results draw inspiration from this formulation, which is of independent interest to Knowledge Representation applications.

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.

Definable group extensions in semi-bounded o-minimal structures

In this note we show: Let R = 〈R, <, +, 0, …〉 be a semi-bounded (respectively, linear) o-minimal expansion of an ordered group, and G a group definable in R of linear dimension m ([2]). Then G is a definable extension of a bounded (respectively, definably compact) definable group B by 〈Rm, +〉 (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Compact domination for groups definable in linear o-minimal structures

We prove the Compact Domination Conjecture for groups definable in linear o-minimal structures. Namely, we show that every definably compact group G definable in a saturated linear o-minimal expansion of an ordered group is compactly dominated by (G/G00, m, π), where m is the Haar measure on G/G00 and π : G → G/G00 is the canonical group homomorphism.

Semilinear stars are contractible

Let

ON DEFINABLE SKOLEM FUNCTIONS IN WEAKLY O-MINIMAL NONVALUATIONAL STRUCTURES

\cal R

Definable quotients of locally definable groups

be an ordered vector space over an ordered division ring. We prove that every definable set

Local analysis for semi-bounded groups

X

Definable groups as homomorphic images of semi-linear and field-definable groups

is a finite union of relatively open definable subsets which are definably simply-connected, settling a conjecture from [5]. The proof goes through the stronger statement that the star of a cell in a special linear decomposition of