Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deciding the Continuum Hypothesis with the Inverse Powerset   We introduce the concept of inverse powerset by adding three axioms to the
Zermelo-Fraenkel set theory. This extends the Zermelo-Fraenkel set theory with
a new type of set which is motivated by an intuitive meaning and interesting
applications. We present different ways to extend the definition of cardinality
and show that one implies the continuum hypothesis while another implies the
negation of the continuum hypothesis. We will also explore the idea of empty
sets of different cardinalities which could be seen as the empty counterpart of
Cantor's theorem for infinite sets.

16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys