| Modulo computably enumerable degrees by cupping partners |
| |
| 作者单位： | Wei WANG （Department of Mathematics, Nanjing University, Nanjing 210093, China） ;De-cheng DING（Department of Mathematics, Nanjing University, Nanjing 210093, China） ; |
| |
| 摘 要： | Cupping partners of an element in an upper semilattice with a greatest element 1 are those joining the element to 1. We define a congruence relation on such an upper semilattice by considering the elements having the same cupping partners as equivalent. It is interesting that this congruence relation induces a non-dense quotient structure of computably enumerable Turing degrees. Another main interesting phenomenon in this article is that on the computably enumerable degrees, this relation is different from that modulo the noncuppable ideal, though they define a same equivalent class for the computable Turing degree.
|
Modulo computably enumerable degrees by cupping partners |
| |
| Wei WANG,De-cheng DING. Modulo computably enumerable degrees by cupping partners[J]. Science in China(Mathematics), 2007, 50(6): 899-912. DOI: 10.1007/s11425-007-0064-x |
| |
| Authors: | Wei WANG De-cheng DING |
| |
| Affiliation: | Department of Mathematics, Nanjing University, Nanjing 210093, China |
| |
| Abstract: | Cupping partners of an element in an upper semilattice with a greatest element 1 are those joining the element to 1. We define a congruence relation on such an upper semilattice by considering the elements having the same cupping partners as equivalent. It is interesting that this congruence relation induces a non-dense quotient structure of computably enumerable Turing degrees. Another main interesting phenomenon in this article is that on the computably enumerable degrees, this relation is different from that modulo the noncuppable ideal, though they define a same equivalent class for the computable Turing degree. |
| |
| Keywords: | Turing degrees computably enumerable cupping partner |
| 本文献已被 万方数据 SpringerLink 等数据库收录！ |
