Definable Relations in the Real Field with a Distinguished Subgroup of the Unit Circle

Characterizing the Multiplicative Group of a Real Closed Field in Terms of its Divisible Maximal Subgroup

Characterization and axiomatization of all semigroups whose square is group

In this paper we give a characterization for all semigroups whose square is a group. Moreover, we axiomatize such semigroups and study some relations between the class of these semigroups and Grouplikes,introduced by the author. Also, we observe that this paper characterizes and axiomatizes a class of Homogroups (semigroups containing an ideal subgroup).  Finally, several equivalent conditions ...

O ct 2 00 9 LOCAL METRIC PROPERTIES AND REGULAR STRATIFICATIONS OF p - ADIC DEFINABLE SETS

— We study the geometry of germs of definable (semialgebraic or subanalytic) sets over a p-adic field from the metric, differential and measure geometric point of view. We prove that the local density of such sets at each of their points does exist. We then introduce the notion of distinguished tangent cone with respect to some open subgroup with finite index in the multiplicative group of our ...

LOCAL METRIC PROPERTIES AND REGULAR STRATIFICATIONS OF p-ADIC DEFINABLE SETS

— We study the geometry of germs of definable (semialgebraic or subanalytic) sets over a p-adic field from the metric, differential and measure geometric point of view. We prove that the local density of such sets at each of their points does exist. We then introduce the notion of distinguished tangent cone with respect to some open subgroup with finite index in the multiplicative group of our ...

Definably Simple Groups in O-minimal Structures

Let G = 〈G, ·〉 be a group definable in an o-minimal structure M. A subset H of G is G-definable if H is definable in the structure 〈G, ·〉 (while definable means definable in the structure M). Assume G has no Gdefinable proper subgroup of finite index. In this paper we prove that if G has no nontrivial abelian normal subgroup, then G is the direct product of G-definable subgroups H1, . . . ,Hk s...