Plus cupping degrees do not form an ideal

Angsheng Li; Yicheng Zhao

doi:10.1360/02yf0347

Plus cupping degrees do not form an ideal

Angsheng Li^*
, Yicheng Zhao

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

A computably enumerable (c.e., for short) degree a is called plus cupping, if every c.e. degree x with 0 < x ≤ a is cuppable. Let PC be the set of all plus cupping degrees. In the present paper, we show that PC is not closed under the join operation v by constructing two plus cupping degrees which join to a high degree. So by the Harrington's noncupping theorem, PC is not an ideal of ε. Copyright by Science in China Press 2004.

Original language	English
Pages (from-to)	635-654
Number of pages	20
Journal	Science in China, Series F: Information Sciences
Volume	47
Issue number	5
DOIs	https://doi.org/10.1360/02yf0347
State	Published - Oct 2004
Externally published	Yes

Keywords

Computably enumerable set
Definability
Turing degree

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10.1360/02yf0347

Cite this

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abstract = "A computably enumerable (c.e., for short) degree a is called plus cupping, if every c.e. degree x with 0 < x ≤ a is cuppable. Let PC be the set of all plus cupping degrees. In the present paper, we show that PC is not closed under the join operation v by constructing two plus cupping degrees which join to a high degree. So by the Harrington's noncupping theorem, PC is not an ideal of ε. Copyright by Science in China Press 2004.",

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AB - A computably enumerable (c.e., for short) degree a is called plus cupping, if every c.e. degree x with 0 < x ≤ a is cuppable. Let PC be the set of all plus cupping degrees. In the present paper, we show that PC is not closed under the join operation v by constructing two plus cupping degrees which join to a high degree. So by the Harrington's noncupping theorem, PC is not an ideal of ε. Copyright by Science in China Press 2004.

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KW - Definability

KW - Turing degree

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Plus cupping degrees do not form an ideal

Abstract

Keywords

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