Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncomputable Spectral Sets   It is possible to enumerate all computer programs. In particular, for every
partial computable function, there is a shortest program which computes that
function. f-MIN is the set of indices for shortest programs. In 1972, Meyer
showed that f-MIN is Turing equivalent to 0'', the halting set with halting set
oracle.
  This paper generalizes the notion of shortest programs, and we use various
measures from computability theory to describe the complexity of the resulting
"spectral sets." We show that under certain Godel numberings, the spectral sets
are exactly the canonical sets 0', 0'', 0''', ... up to Turing equivalence.
This is probably not true in general, however we show that spectral sets always
contain some useful information. We show that immunity, or "thinness" is a
useful characteristic for distinguishing between spectral sets.
  In the final chapter, we construct a set which neither contains nor is
disjoint from any infinite arithmetic set, yet it is 0-majorized and contains a
natural spectral set. Thus a pathological set becomes a bit more friendly.
Finally, a number of interesting open problems are left for the inspired
reader.

8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess