Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A fixed point for the jump operator on structures   Assuming that $0^#$ exists, we prove that there is a structure that can
effectively interpret its own jump. In particular, we get a structure $\mathcal
A$ such that \[ Sp({\mathcal A}) = \{{\bf x}':{\bf x}\in Sp ({\mathcal A})\},
\] where $Sp ({\mathcal A})$ is the set of Turing degrees which compute a copy
of $\mathcal A$.
  It turns out that, more interesting than the result itself, is its unexpected
complexity. We prove that higher-order arithmetic, which is the union of full
$n$th-order arithmetic for all $n$, cannot prove the existence of such a
structure.

27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs