A NOTE ON INITIAL SEGMENTS OF THE ENUMERATION DEGREES

Author:

SLAMAN THEODORE A.,SORBI ANDREA

Abstract

AbstractWe show that no nontrivial principal ideal of the enumeration degrees is linearly ordered: in fact, below every nonzero enumeration degree one can embed every countable partial order. The result can be relativized above any total degree: if a,b are enumeration degrees, with a total, and a < b, then in the degree interval (a,b), one can embed every countable partial order.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference16 articles.

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Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Fragments of the theory of the enumeration degrees;Advances in Mathematics;2021-06

2. S. Barry Cooper (1943–2015);Computability;2018-06-07

3. Density of the cototal enumeration degrees;Annals of Pure and Applied Logic;2018-05

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