Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The typical Turing degree   The Turing degree of a real measures the computational difficulty of
producing its binary expansion. Since Turing degrees are tailsets, it follows
from Kolmogorov's 0-1 law that for any property which may or may not be
satisfied by any given Turing degree, the satisfying class will either be of
Lebesgue measure 0 or 1, so long as it is measurable. So either the
\emph{typical} degree satisfies the property, or else the typical degree
satisfies its negation. Further, there is then some level of randomness
sufficient to ensure typicality in this regard. A similar analysis can be made
in terms of Baire category, where a standard form of genericity now plays the
role that randomness plays in the context of measure.
  We describe and prove a number of results in a programme of research which
aims to establish the properties of the typical Turing degree, where typicality
is gauged either in terms of Lebesgue measure or Baire category.

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The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
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The categories of this paper are: econ
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess