Sequential discontinuity and first-order problems
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916103342522368 |
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| author | Pauly, Arno Soldà, Giovanni |
| author_facet | Pauly, Arno Soldà, Giovanni |
| contents | We explore the low levels of the structure of the continuous Weihrauch degrees of first-order problems. In particular, we show that there exists a minimal discontinuous first-order degree, namely that of $\accn$, without any determinacy assumptions. The same degree is also revealed as the least sequentially discontinuous one, i.e. the least degree with a representative whose restriction to some sequence converging to a limit point is still discontinuous.
The study of games related to continuous Weihrauch reducibility constitutes an important ingredient in the proof of the main theorem. We present some initial additional results about the degrees of first-order problems that can be obtained using this approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12641 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sequential discontinuity and first-order problems Pauly, Arno Soldà, Giovanni Logic Logic in Computer Science General Topology 03D78, 03D30, 54H05 We explore the low levels of the structure of the continuous Weihrauch degrees of first-order problems. In particular, we show that there exists a minimal discontinuous first-order degree, namely that of $\accn$, without any determinacy assumptions. The same degree is also revealed as the least sequentially discontinuous one, i.e. the least degree with a representative whose restriction to some sequence converging to a limit point is still discontinuous. The study of games related to continuous Weihrauch reducibility constitutes an important ingredient in the proof of the main theorem. We present some initial additional results about the degrees of first-order problems that can be obtained using this approach. |
| title | Sequential discontinuity and first-order problems |
| topic | Logic Logic in Computer Science General Topology 03D78, 03D30, 54H05 |
| url | https://arxiv.org/abs/2401.12641 |