Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Third-order functionals on partial combinatory algebras   Computability relative to a partial function $f$ on the natural numbers can
be formalized using the notion of an oracle for this function $f$. This can be
generalized to arbitrary partial combinatory algebras, yielding a notion of
`adjoining a partial function to a partial combinatory algebra $A$'. A similar
construction is known for second-order functionals, but the third-order case is
more difficult. In this paper, we prove several results for this third-order
case. Given a third-order functional $\Phi$ on a partial combinatory algebra
$A$, we show how to construct a partial combinatory algebra $A[\Phi]$ where
$\Phi$ is `computable', and which has a `lax' factorization property. Moreover,
we show that, on the level of first-order functions, the effect of making a
third-order functional computable can be described as adding an oracle for a
first-order function.

28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
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The categories of this paper are: stat
10
The categories of this paper are: q-bio
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The categories of this paper are: eess