Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Is set theory indispensable?   Although Zermelo-Fraenkel set theory (ZFC) is generally accepted as the
appropriate foundation for modern mathematics, proof theorists have known for
decades that virtually all mainstream mathematics can actually be formalized in
much weaker systems which are essentially number-theoretic in nature. Feferman
has observed that this severely undercuts a famous argument of Quine and Putnam
according to which set theoretic platonism is validated by the fact that
mathematics is "indispensable" for some successful scientific theories (since
in fact ZFC is not needed for the mathematics that is currently used in
science).
  I extend this critique in three ways: (1) not only is it possible to
formalize core mathematics in these weaker systems, they are in important ways
better suited to the task than ZFC; (2) an improved analysis of the
proof-theoretic strength of predicative theories shows that most if not all of
the already rare examples of mainstream theorems whose proofs are currently
thought to require metaphysically substantial set-theoretic principles actually
do not; and (3) set theory itself, as it is actually practiced, is best
understood in formalist, not platonic, terms, so that in a real sense *set
theory is not even indispensable for set theory*. I also make the point that
even if ZFC is consistent, there are good reasons to suspect that some
number-theoretic assertions provable in ZFC may be false. This suggests that
set theory should not be considered central to mathematics.

37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph