Ja n 20 09 Triangulation in o - minimal fields with standard part map
نویسنده
چکیده
In answering questions from [7] we prove a triangulation result that is of independent interest. In more detail, let R be an o-minimal field with a proper convex subring V , and let st : V → k be the corresponding standard part map. Under a mild assumption on (R, V) we show that definable sets X ⊆ V n admit a triangulation that induces a triangulation of its standard part st(X) ⊆ k n .
منابع مشابه
Differential Equations over Polynomially Bounded O-minimal Structures
We investigate the asymptotic behavior at +∞ of non-oscillatory solutions to differential equations y′ = G(t, y), t > a, where G : R1+l → Rl is definable in a polynomially bounded o-minimal structure. In particular, we show that the Pfaffian closure of a polynomially bounded o-minimal structure on the real field is levelled. A classical topic in asymptotic analysis is the study of the behavior ...
متن کاملTransseries and Todorov-Vernaeve's asymptotic fields
We study the relationship between fields of transseries and residue fields of convex subrings of non-standard extensions of the real numbers. This was motivated by a question of Todorov and Vernaeve, answered in this paper. In this note we answer a question by Todorov and Vernaeve (see, e.g., [35]) concerning the relationship between the field of logarithmic-exponential series from [14] and the...
متن کاملJa n 20 09 Bounds for the return probability of the delayed random walk on finite percolation clusters in the critical case
By an eigenvalue comparison-technique[20], the expected return probability of the delayed random walk on critical Bernoulli bond percolation clusters on the twodimensional Euclidean lattice is estimated. The results are generalised to invariant percolations on unimodular graphs with almost surely finite clusters. The approach involves using the special property of cartesian products of finite g...
متن کاملar X iv : h ep - t h / 05 01 08 5 v 1 1 1 Ja n 20 05 Scalar and Vector Massive Fields in Lyra ’ s Manifold ∗
The problem of coupling between spin and torsion is analysed from a Lyra's manifold background for scalar and vector massive fields using the Duffin-Kemmer-Petiau (DKP) theory. We found the propagation of the torsion is dynamical, and the minimal coupling of DKP field corresponds to a non-minimal coupling in the standard Klein-Gordon-Fock and Proca approaches. The origin of this difference in t...
متن کاملar X iv : 0 90 1 . 18 06 v 1 [ m at h . A G ] 1 3 Ja n 20 09 GREENBERG APPROXIMATION AND THE GEOMETRY OF ARC SPACES
We study the differential properties of generalized arc schemes and geometric versions of Kolchin’s Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.
متن کامل