تقرير
Sequential discontinuity and first-order problems
| العنوان: | Sequential discontinuity and first-order problems |
|---|---|
| المؤلفون: | Pauly, Arno, Soldà, Giovanni |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Logic, Computer Science - Logic in Computer Science, Mathematics - General Topology, 03D78, 03D30, 54H05 |
| الوصف: | 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. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.12641 |
| رقم الأكسشن: | edsarx.2401.12641 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |