A join theorem for the computably enumerable degrees期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

A join theorem for the computably enumerable degrees

Authors:	Carl G Jockusch Jr Angsheng Li Yue Yang

Institution:	Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, Illinois 61801 ; Institute of Software, Chinese Academy of Sciences, P. O. Box 8718, Beijing, 100080, People's Republic of China ; Department of Mathematics, Faculty of Science, National University of Singapore, Lower Kent Ridge Road, Singapore 119260

Abstract:	It is shown that for any computably enumerable (c.e.) degree $\mathbf{w}$ , if $\mathbf{w\not=0}$ , then there is a c.e. degree $\mathbf{a}$ such that $\mathbf{(a\lor w)'} = \mathbf{a'}= \mathbf{0'}$ (so $\mathbf{a}$ is lowand $\mathbf{a\lor w}$ is high). It follows from this and previous work of P. Cholak, M. Groszek and T. Slaman that the low and low c.e. degrees are not elementarily equivalent as partial orderings.

Keywords:	Join theorem computably enumerable degree definable ideals Turing jump

	点击此处可从《Transactions of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Transactions of the American Mathematical Society》下载免费的PDF全文