Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramsey-like theorems and moduli of computation   Ramsey's theorem asserts that every $k$-coloring of $[\omega]^n$ admits an
infinite monochromatic set. Whenever $n \geq 3$, there exists a computable
$k$-coloring of $[\omega]^n$ whose solutions compute the halting set. On the
other hand, for every computable $k$-coloring of $[\omega]^2$ and every
non-computable set $C$, there is an infinite monochromatic set $H$ such that $C
\not \leq_T H$. The latter property is known as cone avoidance.
  In this article, we design a natural class of Ramsey-like theorems
encompassing many statements studied in reverse mathematics. We prove that this
class admits a maximal statement satisfying cone avoidance and use it as a
criterion to re-obtain many existing proofs of cone avoidance. This maximal
statement asserts the existence, for every $k$-coloring of $[\omega]^n$, of an
infinite subdomain $H \subseteq \omega$ over which the coloring depends only on
the sparsity of its elements. This confirms the intuition that Ramsey-like
theorems compute Turing degrees only through the sparsity of its solutions.

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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
1
The categories of this paper are: cs
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The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: q-alg