Density of the Medvedev lattice of Π01 classes

被引：20
|
作者：
Cenzer, D
Hinman, PG
机构：
[1] Univ Florida, Dept Math, Gainesville, FL 32611 USA
[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
来源：
ARCHIVE FOR MATHEMATICAL LOGIC | 2003年 / 42卷 / 06期
关键词：
degree of difficulty; Medvedev lattice; recursive functional; density;
D O I：
10.1007/s00153-002-0166-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The partial ordering of Medvedev reducibility restricted to the family of Pi(1)(0) classes is shown to be dense. For two disjoint computably enumerable sets, the class of separating sets is an important example of a Pi(1)(0) class, which we call a "c.e. separating class". We show that there are no non-trivial meets for c.e. separating classes, but that the density theorem holds in the sublattice generated by the c.e. separating classes.
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页码：583 / 600
页数：18
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