Monotone and 1–1 sets

Journal of the Australian Mathematical Society

D. B. Madan¹ 

[1] R. W. Robinson

关键词: 03 D 25;   

DOI  :  10.1017/S1446788700017626

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

An infinite subset of ω is monotone (1–1) if every recursive function is eventually monotone on it (eventually constant on it or eventually 1–1 on it). A recursively enumerable set is co-monotone (co-1–1) just if its complement is monotone (1–1). It is shown that no implications hold among the properties of being cohesive, monotone, or 1–1, though each implies r-cohesiveness and dense immunity. However it is also shown that co-monotone and co-1–1 are equivalent, that they are properly stronger than the conjunction of r-maximality and dense simplicity, and that they do not imply maximality.

【 授权许可】

Unknown