Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple finitary proof of Goodstein's Theorem   We assumed that, for every natural number k, there is a natural number u such
that the (k-1)th term of G(u) is k^k, and that G(u) terminates finitely. It
immediately follows that every Goodstein Sequence G(m) over the natural numbers
must terminate finitely.
  The assumption is easily seen to be false since there is no m such that the
third term of g(m) is 4^4.

15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org