Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Consequences of arithmetic for set theory   In this paper, we consider certain cardinals in ZF (set theory without AC,
the Axiom of Choice). In ZFC (set theory with AC), given any cardinals C and D,
either C <= D or D <= C. However, in ZF this is no longer so. For a given
infinite set A consider Seq(A), the set of all sequences of A without
repetition. We compare |Seq(A)|, the cardinality of this set, to |P(A)|, the
cardinality of the power set of A.
  What is provable about these two cardinals in ZF? The main result of this
paper is that
  ZF |- for all A: |Seq(A)| not= |P(A)|
  and we show that this is the best possible result.
  Furthermore, it is provable in ZF that if B is an infinite set, then
|fin(B)|<|P(B)|, even though the existence for some infinite set B^* of a
function f from fin(B^*) onto P(B^*) is consistent with ZF.

8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph