Low sets without subsets of higher many-one degree

被引：2
|
作者：
Cintioli, Patrizio [1 ]
机构：
[1] Univ Camerino, Dipartimento Matemat & Informat, I-62032 Camerino, Italy
来源：
MATHEMATICAL LOGIC QUARTERLY | 2011年 / 57卷 / 05期
关键词：
Recursively enumerable sets; low sets; many-one degrees; finite-injury method;
D O I：
10.1002/malq.200920043
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Given a reducibility <=(r), we say that an infinite set A is r-introimmune if A is not r-reducible to any of its subsets B with vertical bar A\B vertical bar = infinity. We consider the many-one reducibility <=(m) and we prove the existence of a low(1) m-introimmune set in Pi(0)(1) and the existence of a low(1) bi-m-introimmune set. (C) 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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页码：517 / 523
页数：7
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