This paper studies type-definable groups in C-minimal structures. We show first for some of these groups, that they contain a cone which is a subgroup. This result will be applied to show that in any geometric locally modular non trivial C-minimal structure, there is a definable infinite C-minimal group.

In this paper we present some examples of decision procedures based on tableau calculus for some monoand multimodal logics having a semantics involving properties that are not easily representable in tree-like structures (like e.g. density, confluence and persistence). We show how to handle them in our framework by generalizing usual tableaux (which are trees) to richer structures: rooted direc...

In this paper, we consider the minimal cell structure problem forGCW complexes. A CW complex is a nice approximation of general topological spaces, which is constructed by repeating attaching higher dimensional cells to lower ones. A G-CW complex is its generalized version to spaces with a group action. The structure theorem for ordinary CW complexes is well-studied, and we can know the minimal...

The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of “small definable set” plays a special role in this description. Introduction. In a classical paper [8] A. Robinson proved the completeness of the theory of real closed fields with a predicate for a proper dense real closed subfi...

The open core of an expansion of a dense linear order is its reduct, in the sense of definability, generated by the collection of all of its open definable sets. In this paper, expansions of dense linear orders that have o-minimal open core are investigated, with emphasis on expansions of densely ordered groups. The first main result establishes conditions under which an expansion of a densely ...

Let M be a structure in some language. Assume M has elimination of imaginaries. Let X be a definable set. Definable will mean “definable with parameters.” By a definable topology, we mean a definable family of subsets {By ⊂ X}y∈Y which form the basis for some topology on X. The fact that these form a basis for a topology amounts to the claim that if y1, y2 have By1 ∩By2 6= ∅, then for every x ∈...

Peano differentiability generalizes ordinary differentiability to higher order. There are two ways to define Peano differentiability for functions defined on non-open sets. For both concepts, we investigate the question under which conditions a function defined on a closed set can be extended to a Peano differentiable function on the ambient space if the sets and functions are definable in an o...

In this paper we develop tame topology over dp-minimal structures equipped with definable uniformities satisfying certain assumptions. Our assumptions are enough to ensure that definable sets are tame: there is a good notion of dimension on definable sets, definable functions are almost everywhere continuous, and definable sets are finite unions of graphs of definable continuous “multi-valued f...

More and more data (documents) are wrapped in XML format. Mining these documents involves mining the corresponding XML structures. However, the semi-structured (tree structured) XML makes it somewhat difficult for traditional data mining algorithms to work properly. Recently, several new algorithms were proposed to mine XML documents. These algorithms mainly focus on mining frequent tree struct...

Here we prove a Poincaré Verdier duality theorem for the ominimal sheaf cohomology with definably compact supports of definably normal, definably locally compact spaces in an arbitrary o-minimal structure. RÉSUMÉ. On démontre une dualité de Poincaré Verdier dans le cadre de la cohomologie o-minimale des faisceaux avec support compact et définissable sur un espace définissablement normaux, défin...