Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Denseness results in the theory of algebraic fields   We study when the property that a field is dense in its real and p-adic
closures is elementary in the language of rings and deduce that all models of
the theory of algebraic fields have this property.

16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs