Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: What is the real category of sets?   Category theory provides a powerful tool to organize mathematics. A sample of
this descriptive power is given by the categorical analysis of the practice of
"classes as shorthands" in ZF set theory. In this case category theory provides
a natural way to describe the relation between mathematics and metamathematics:
if metamathematics can be described by using categories (in particular
syntactic categories), then the mathematical level is represented by internal
categories. Through this two-level interpretation we can clarify the relation
between classes and sets in ZF and, in particular, we can present two
equivalent categorical notions of definable set. Some common sayings about set
theory will be interpreted in the light of this representation, emphasizing the
distinction between naive and rigorous sentences about sets and classes.

26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th