Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parametric Church's Thesis: Synthetic Computability without Choice   In synthetic computability, pioneered by Richman, Bridges, and Bauer, one
develops computability theory without an explicit model of computation. This is
enabled by assuming an axiom equivalent to postulating a function $\phi$ to be
universal for the space $\mathbb{N}\to\mathbb{N}$ ($\mathsf{CT}_\phi$, a
consequence of the constructivist axiom $\mathsf{CT}$), Markov's principle, and
at least the axiom of countable choice. Assuming $\mathsf{CT}$ and countable
choice invalidates the law of excluded middle, thereby also invalidating
classical intuitions prevalent in textbooks on computability. On the other
hand, results like Rice's theorem are not provable without a form of choice. In
contrast to existing work, we base our investigations in constructive type
theory with a separate, impredicative universe of propositions where countable
choice does not hold and thus a priori $\mathsf{CT}_{\phi}$ and the law of
excluded middle seem to be consistent. We introduce various parametric
strengthenings of $\mathsf{CT}_{\phi}$, which are equivalent to assuming
$\mathsf{CT}_\phi$ and an $S^m_n$ operator for $\phi$ like in the $S^m_n$
theorem. The strengthened axioms allow developing synthetic computability
theory without choice, as demonstrated by elegant synthetic proofs of Rice's
theorem. Moreover, they seem to be not in conflict with classical intuitions
since they are consequences of the traditional analytic form of $\mathsf{CT}$.
  Besides explaining the novel axioms and proofs of Rice's theorem we
contribute machine-checked proofs of all results in the Coq proof assistant.

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The categories of this paper are: plasm-ph
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat