Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On power sets   This work presents theorems which state (i) Z is a proper subset for any
bijection f between A and Z, where Z is contained in P(A), A is a non-finite
set and |Z|=|A|, and (ii) being Z a proper subset of P(A) nothing affirms or
denies that |P(A)|>|A|. Russell's paradox is examined and it is shown that the
set of all the ordinary sets does not exist. A mistake in Cantor's proof on
cardinality of power sets is shown.

5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an