Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The elementary closure of the class Nr_nCA_m for m\geq n+1 is not
  finitely axiomatizable, futhermore for any finite k\geq 1, there is A\in
  Nr_{\omega}CA_{\omeg+k}that is not SNr_{\omega}CA_{\omega+k+1}
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph