On Regressive Isols and Comparability of Summands and a Theorem of R. Downey
作者:
Joseph Barback,
期刊:
Mathematical Logic Quarterly
(WILEY Available online 1997)
卷期:
Volume 43,
issue 1
页码: 83-91
ISSN:0942-5616
年代: 1997
DOI:10.1002/malq.19970430111
出版商: WILEY‐VCH Verlag Berlin GmbH
关键词: Isols;Regressive isols;Hyper‐torre isols
数据来源: WILEY
摘要:
AbstractIn this paper we present a collection of results related to the comparability of summands property of regressive isols. We show that if an infinite regressive isol has comparability of summands, then every predecessor of the isol has a weak comparability of summands property. Recently R. Downey proved that there exist regressive isols that are both hyper‐torre and cosimple. There is a surprisingly close connection between non‐recursive recursively enumerable sets and particular retraceable sets and regressive isols. We apply the theorem of Downey to show that among the regressive isols that are related to recursively enumerable sets there are some with a new prope
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