Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Forcing the $\Pi^1_3$-Reduction Property and a Failure of
  $\Pi^1_3$-Uniformization   We force over the constructible universe to obtain a model of the
$\Pi^1_3$-reduction property, thus lowering the best known large cardinal
strength from the existence of $M_1^{\#}$ to just ZFC. In this model the
$\Pi^1_3$-uniformization property fails, which separates these two principles
for the first time.

23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org