Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Herbrand Functional Interpretation of the Double Negation Shift   This paper considers a generalisation of selection functions over an
arbitrary strong monad $T$, as functionals of type $J^T_R X = (X \to R) \to T
X$. It is assumed throughout that $R$ is a $T$-algebra. We show that $J^T_R$ is
also a strong monad, and that it embeds into the continuation monad $K_R X = (X
\to R) \to R$. We use this to derive that the explicitly controlled product of
$T$-selection functions is definable from the explicitly controlled product of
quantifiers, and hence from Spector's bar recursion. We then prove several
properties of this product in the special case when $T$ is the finite power set
monad ${\mathcal P}(\cdot)$. These are used to show that when $T X = {\mathcal
P}(X)$ the explicitly controlled product of $T$-selection functions calculates
a witness to the Herbrand functional interpretation of the double negation
shift.

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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: econ
27
The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
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The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: stat