Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On analytic functions in an ordered field with an infinite rank
  valuation   Let K be the scalar field of the first orthomodular (or Form Hilbert) space,
described by H. Keller in 1980. It has a non-Archimedean order, an infinite
rank valuation compatible with the order as well as an explicitly defined
ultrametric, all of which induce the same topology. We study analytic functions
defined on valued field K, and we will establish an invertibility local theorem
for these functions as an application of Banach fixed point theorem.

23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics