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Searching for an analogue of ATR in the Weihrauch lattice
arXiv - CS - Logic in Computer Science Pub Date : 2018-12-04 , DOI: arxiv-1812.01549
Takayuki Kihara, Alberto Marcone, Arno Pauly

There are close similarities between the Weihrauch lattice and the zoo of axiom systems in reverse mathematics. Following these similarities has often allowed researchers to translate results from one setting to the other. However, amongst the big five axiom systems from reverse mathematics, so far ATR_0 has no identified counterpart in the Weihrauch degrees. We explore and evaluate several candidates, and conclude that the situation is complicated.

中文翻译:

在 Weihrauch 格子中寻找 ATR 的类似物

Weihrauch 格和逆向数学中的公理系统动物园之间有密切的相似之处。遵循这些相似性通常允许研究人员将结果从一种设置转换为另一种设置。然而,在逆向数学的五大公理系统中,到目前为止,ATR_0 在 Weihrauch 度中还没有确定的对应物。我们探索和评估了几个候选人,得出的结论是情况复杂。
更新日期:2020-01-14
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