Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Model theoretic properties of the Urysohn sphere   We characterize model theoretic properties of the Urysohn sphere as a metric
structure in continuous logic. In particular, our first main result shows that
the theory of the Urysohn sphere is $\text{SOP}_n$ for all $n\geq 3$, but does
not have the fully finite strong order property. Our second main result is a
geometric characterization of dividing independence in the theory of the
Urysohn sphere. We further show that this characterization satisfies the
extension axiom, and so forking and dividing are the same for complete types.
Our results require continuous analogs of several tools and notions in
classification theory. While many of these results are undoubtedly known to
researchers in the field, they have not previously appeared in publication.
Therefore, we include a full exposition of these results for general continuous
theories.

21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
19
The categories of this paper are: eess
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an