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THE CHARACTERIZATION OF WEIHRAUCH REDUCIBILITY IN SYSTEMS CONTAINING
The Journal of Symbolic Logic ( IF 0.5 ) Pub Date : 2020-10-27 , DOI: 10.1017/jsl.2020.53 PATRICK UFTRING
The Journal of Symbolic Logic ( IF 0.5 ) Pub Date : 2020-10-27 , DOI: 10.1017/jsl.2020.53 PATRICK UFTRING
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.
中文翻译:
包含系统的 Weihrauch 可还原性的表征
我们将 Weihrauch 可还原性描述为$ \operatorname {\mathrm {E-PA^{\omega }}} + \operatorname {\mathrm {QF-AC^{0,0}}}$ 以及通过使用哥德尔辩证法解释的修改,结合线性逻辑、非标准算术、高阶可计算性和相位语义的思想,在同一微积分的线性变体中通过可证明性包含它的所有系统。
更新日期:2020-10-27
中文翻译:
包含系统的 Weihrauch 可还原性的表征
我们将 Weihrauch 可还原性描述为