Further Thoughts on Definability in the Urysohn Sphere
نویسنده
چکیده
We discuss some basic geometry of sets definable in the Urysohn sphere using only finitely many parameters and briefly remark on the case of arbitrary definable sets. Then we discuss definable functions in the Urysohn sphere satisfying a special syntactic property.
منابع مشابه
Definable Functions in Urysohn’s Metric Space
Let U denote the Urysohn sphere and consider U as a metric structure in the empty continuous signature. We prove that every definable function U → U is either a projection function or else has relatively compact range. As a consequence, we prove that many functions natural to the study of the Urysohn sphere are not definable. We end with further topological information on the range of the defin...
متن کاملThe Urysohn Sphere Is Oscillation Stable
We solve the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for `2 in the context of the Urysohn space U. This is achieved by solving a purely combinatorial problem involving a family of countable ultrahomogeneous metric spaces with finitely many dis-
متن کامل. M G ] 9 J un 2 00 7 THE OSCILLATION STABILITY PROBLEM FOR THE URYSOHN SPHERE : A COMBINATORIAL APPROACH
We study the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for ℓ 2 in the context of the Urysohn space U. In particular, we show that this problem reduces to a purely combinatorial problem involving a family of countable ultrahomogeneous metric spaces with finitely many distances.
متن کاملThe Urysohn Sphere Is Pseudofinite
We show that the Urysohn sphere is pseudofinite. As a consequence, we derive an approximate 0-1 law for finite metric spaces of diameter at most 1.
متن کاملar X iv : 0 70 6 . 13 26 v 3 [ m at h . M G ] 2 7 Fe b 20 09 THE OSCILLATION STABILITY PROBLEM FOR THE URYSOHN SPHERE : A COMBINATORIAL APPROACH
We study the oscillation stability problem for the Urysohn sphere, an analog of the distortion problem for ℓ 2 in the context of the Urysohn space U. In particular, we show that this problem reduces to a purely combinatorial problem involving a family of countable ultrahomogeneous metric spaces with finitely many distances.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012