Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete orderings in the real spectrum   We study discrete orderings in the real spectrum of a commutative ring by
defining discrete prime cones and give an algebro-geometric meaning to some
kind of diophantine problems over discretely ordered rings. Also for a
discretely ordered ring $M$ and a real closed field $R$ containing $M$ we prove
a theorem on the distribution of the discrete orderings of $M[X_1,\dots,X_n]$
in $\Spec(R[X_1,\dots,X_n])$ in geometric terms. To be more precise, we prove
that any ball $\mathbb{B}(\alpha,r)$ in $\Spec(R[X_1,\dots,X_n]$) with center
$\alpha$ and radius $r$ (defined via Robson's metric) contains a discrete
ordering of $M[X_1,\dots,X_n]$ whenever $r$ is non-infinitesimal and $\alpha$
is away from all hyperplanes over $M$ passing through the origin.

4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics