Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New relations and separations of conjectures about incompleteness in the
  finite domain   Our main results are in the following three sections:
  1. We prove new relations between proof complexity conjectures that are
discussed in \cite{pu18}.
  2. We investigate the existence of p-optimal proof systems for
$\mathsf{TAUT}$, assuming the collapse of $\cal C$ and $\sf N{\cal C}$ (the
nondeterministic version of $\cal C$) for some new classes $\cal C$ and also
prove new conditional independence results for strong theories, assuming
nonexistence of p-optimal proof systems.
  3. We construct two new oracles ${\cal V}$ and ${\cal W}$. These two oracles
imply several new separations of proof complexity conjectures in relativized
worlds. Among them, we prove that existence of a p-optimal proof system for
$\mathsf{TAUT}$ and existence of a complete problem for $\mathsf{TFNP}$ are
independent of each other in relativized worlds which was not known before.

13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn