Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Recursion-Theoretic Ranking and Compression   For which sets A does there exist a mapping, computed by a total or partial
recursive function, such that the mapping, when its domain is restricted to A,
is a 1-to-1, onto mapping to $\Sigma^*$? And for which sets A does there exist
such a mapping that respects the lexicographical ordering within A? Both cases
are types of perfect, minimal hash functions. The complexity-theoretic versions
of these notions are known as compression functions and ranking functions. The
present paper defines and studies the recursion-theoretic versions of
compression and ranking functions, and in particular studies the question of
which sets have, or lack, such functions. Thus, this is a case where, in
contrast to the usual direction of notion transferal, notions from complexity
theory are inspiring notions, and an investigation, in computability theory.
  We show that the rankable and compressible sets broadly populate the
1-truth-table degrees, and we prove that every nonempty coRE cylinder is
recursively compressible.

17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat