Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The reverse mathematics of Cousin's lemma   Cousin's lemma is a compactness principle that naturally arises when studying
the gauge integral, a generalisation of the Lebesgue integral. We study the
axiomatic strength of Cousin's lemma for various classes of functions, using
Friedman and Simpson's reverse mathematics in second-order arithmetic. We prove
that, over $\mathsf{RCA}_0$:
  (i) Cousin's lemma for continuous functions is equivalent to the system
$\mathsf{WKL}_0$;
  (ii) Cousin's lemma for Baire 1 functions is at least as strong as
$\mathsf{ACA}_0$;
  (iii) Cousin's lemma for Baire 2 functions is at least as strong as
$\mathsf{ATR}_0$.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph