Degrees of incomputability, realizability and constructive reverse mathematics
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866913821048700928 |
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| author | Kihara, Takayuki |
| author_facet | Kihara, Takayuki |
| contents | There is a way of assigning a realizability notion to each degree of incomputability. In our setting, we make use of Weihrauch degrees (degrees of incomputability/discontinuity of partial multi-valued functions) to obtain Lifschitz-like relative realizability predicates. In this note, we present sample examples on how to lift some separation results on Weihrauch degrees to those over intuitionistic Zermelo-Fraenkel set theory ${\bf IZF}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2002_10712 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Degrees of incomputability, realizability and constructive reverse mathematics Kihara, Takayuki Logic Logic in Computer Science There is a way of assigning a realizability notion to each degree of incomputability. In our setting, we make use of Weihrauch degrees (degrees of incomputability/discontinuity of partial multi-valued functions) to obtain Lifschitz-like relative realizability predicates. In this note, we present sample examples on how to lift some separation results on Weihrauch degrees to those over intuitionistic Zermelo-Fraenkel set theory ${\bf IZF}$. |
| title | Degrees of incomputability, realizability and constructive reverse mathematics |
| topic | Logic Logic in Computer Science |
| url | https://arxiv.org/abs/2002.10712 |