Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recursion and the Axiom of Infinity   This paper examines the completion of an w-ordered sequence of recursive
definitions which on the one hand defines an increasing sequence of nested set
and on the other redefines successively a numeric variable as the cardinal of
the successively defined nested sets. The consequence is a contradiction
involving the consistency of w-order and then that of the Axiom of Infinity.

31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph