Title: | 加杯图灵度的一个层谱 |
Author: | 王勇
|
Issued Date: | 2003
|
Major: | 基础数学
|
Degree Grantor: | 中国科学院软件研究所
|
Place of Degree Grantor: | 中国科学院软件研究所
|
Degree Level: | 博士
|
Keyword: | 图灵度
; 计算可枚举度
; 可杯
; 加杯
|
Abstract: | 本文研究计算可枚举图灵度的结构,提出并完成了一个加杯层谱的证明。计算可枚举度(computably,enumerable,c.e.degree)a被称作加杯的(plus cupping),若对任何c.e.度x,o<x三a,存在ce.度v≠0',满足x v y=0'。我们称一个c.e.度是仆加杯的(n-pls-cupping),如果对每个c.e.度x,0<x≤a,存在lownc.e度1,有xVI=0'。定义Pc和Pcn分别为所有的加杯和n-加杯c.e.度的集合。我们有PC1 lis contained in PC2 lis contained in PC3=PC。在这篇文章中,我们证明了PCI c PCZ,从而给出了加杯计算可枚举图灵度的一个非平凡层谱。该定理扩充了李昂生、吴国华、张再跃2000年提出的一个层谱:LC1 C LC2 9 LC3=CUP,同时也扩充了Harrington1978年的加杯定理(Plus Cupping Theorem)。 |
English Abstract: | We study the structure of the plus cupping Turing degrees in this paper. A computable enumerable (c.e. ) degree a is called plus cupping, if for every c.e. degree x with 0 < x < a, there is a c.e. degree y ≠ 0' such that x V y = 0'. We say that a is n-plus-cupping, if for every c.e. degree x, if 0 < x < a, then there is a lown c.e. degree 1 such that x V 1 = 0'. Let PC and PCn be the set of all plus-cupping, and n-plus-cupping c.e. degrees respectively. Then PCi C PC2 C PC3 = PC. In this paper we show that PCi C PC2, so giving a nontrivial hierarchy for the plus cupping degrees. The theorem also extends the result of Li, Wu and Zhang's theorem in 2000 [20] LC1 C LC2 C LC3 = CUP, as well as extending the Harrington plus-cupping theorem in 1978. |
Language: | 中文
|
Content Type: | 学位论文
|
URI: | http://ir.iscas.ac.cn/handle/311060/6908
|
Appears in Collections: | 中科院软件所
|
File Name/ File Size |
Content Type |
Version |
Access |
License |
|
LW011260.pdf(1410KB) | -- | -- | 限制开放 | -- | 联系获取全文 |
|
Recommended Citation: |
王勇. 加杯图灵度的一个层谱[D]. 中国科学院软件研究所. 中国科学院软件研究所. 2003-01-01.
|
|
|