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On Regressive Isols and Comparability of Summands and a Theorem of R. Downey

✍ Scribed by Joseph Barback

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 508 KB
Volume: 43
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.19970430111

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✦ Synopsis

Abstract

In 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 property.

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