Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Universally defining finitely generated subrings of global fields   It is shown that any finitely generated subring of a global field has a
universal first-order definition in its fraction field. This covers
Koenigsmann's result for the ring of integers and its subsequent extensions to
rings of integers in number fields and rings of $S$-integers in global function
fields of odd characteristic. In this article a proof is presented which is
uniform in all global fields, including the characteristic two case, where the
result is entirely novel. Furthermore, the proposed method results in universal
formulae requiring significantly fewer quantifiers than the formulae that can
be derived through the previous approaches.

19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs