D-MAXIMAL SETS

被引：1

作者：

Cholak, Peter A. ^{[1
]}

Gerdes, Peter ^{[1
]}

Lange, Karen ^{[2
]}

机构：

[1] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA

[2] Wellesley Coll, Dept Math, Wellesley, MA 02181 USA

来源：

JOURNAL OF SYMBOLIC LOGIC | 2015年 / 80卷 / 04期

关键词：

computably enumerable sets under inclusion; maximal sets; r-maximal sets; hhsimple sets; RECURSIVELY-ENUMERABLE SETS; ELEMENTARY THEORY; LATTICE; ORBITS; AUTOMORPHISMS;

D O I：

10.1017/jsl.2015.3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Soare [20] proved that the maximal sets for man orbit in epsilon. We consider here D-maximal sets, generalizations of maximal sets introduced by Herrmann and Kummer [12]. Some orbits of D-maximal sets are well understood, e.g., hemimaximal sets [8], but many are not. The goal of this paper is to define new invariants on computably enumerable sets and to use them to give a complete nontrivial classification of the D-maximal sets. Although these invariants help us to better understand the D-maximal sets, we use them to show that several classes of D-maximal sets break into infinitely many orbits.

引用

页码：1182 / 1210

页数：29