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THE CHARACTERIZATION OF WEIHRAUCH REDUCIBILITY IN SYSTEMS CONTAINING $E-PA^{\omega } + QF-AC^{0,0}$

Published online by Cambridge University Press:  27 October 2020

PATRICK UFTRING*
Affiliation:
DEPARTMENT OF MATHEMATICS TECHNISCHE UNIVERSITÄT DARMSTADT SCHLOSSGARTENSTRAßE 7 64289DARMSTADT, GERMANYE-mail: patrick_juergen.uftring@stud.tu-darmstadt.de

Abstract

We characterize Weihrauch reducibility in $ \operatorname {\mathrm {E-PA^{\omega }}} + \operatorname {\mathrm {QF-AC^{0,0}}}$ and all systems containing it by the provability in a linear variant of the same calculus using modifications of Gödel’s Dialectica interpretation that incorporate ideas from linear logic, nonstandard arithmetic, higher-order computability, and phase semantics.

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© The Association for Symbolic Logic 2020

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THE CHARACTERIZATION OF WEIHRAUCH REDUCIBILITY IN SYSTEMS CONTAINING $E-PA^{\omega } + QF-AC^{0,0}$
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