Embeddings into the Medvedev and Muchnik lattices of Π01 classes

被引：26

作者：

Binns, S ^{[1
]}

Simpson, SG ^{[1
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

ARCHIVE FOR MATHEMATICAL LOGIC | 2004年 / 43卷 / 03期

关键词：

Distributive Lattice; Medvedev Degree; Muchnik Lattice; Medvedev Reducibility; Countable Distributive Lattice;

D O I：

10.1007/s00153-003-0195-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let P-w and P-M be the countable distributive lattices of Muchnik and Medvedev degrees of non-empty Pi(1)(0) subsets of 2(omega), under Muchnik and Medvedev reducibility, respectively. We show that all countable distributive lattices are lattice-embeddable below any non-zero element of P-w. We show that many countable distributive lattices are lattice-embeddable below any non-zero element of P-M.

引用

页码：399 / 414

页数：16

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