Q 1-degrees of c.e. sets

被引：13

作者：

Omanadze, R. Sh. ^{[1
]}

Chitaia, I. O. ^{[1
]}

机构：

[1] Iv Javakhishvili Tbilisi State Univ, GE-0186 Tbilisi, Georgia

来源：

ARCHIVE FOR MATHEMATICAL LOGIC | 2012年 / 51卷 / 5-6期

基金：

美国国家科学基金会;

关键词：

Q(1)-reducibility; s-reducibility; Hyperhypersimple set; Hemimaximal set; LATTICE;

D O I：

10.1007/s00153-012-0278-7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that the Q-degree of a hyperhypersimple set includes an infinite collection of Q (1)-degrees linearly ordered under with order type of the integers and consisting entirely of hyperhypersimple sets. Also, we prove that the c.e. Q (1)-degrees are not an upper semilattice. The main result of this paper is that the Q (1)-degree of a hemimaximal set contains only one c.e. 1-degree. Analogous results are valid for s (1)-degrees.

引用

页码：503 / 515

页数：13

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