On the existence of a strong minimal pair-Reference-Cited by-同舟云学术

On the existence of a strong minimal pair

Published:2015-06 Issue:01 Volume:15 Page:1550003
ISSN:0219-0613
Container-title:Journal of Mathematical Logic
language:en
Short-container-title:J. Math. Log.

Author:

Barmpalias George¹²,Cai Mingzhong³,Lempp Steffen⁴,Slaman Theodore A.⁵

Affiliation:

1. State Key Lab of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, P. R. China

2. School of Mathematics, Statistics and Operations Research, Victoria University, Wellington, New Zealand

3. Department of Mathematics, Dartmouth College, Hanover, NH 03755, USA

4. Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA

5. Department of Mathematics, University of California, Berkeley, CA 94720, USA

Abstract

We show that there is a strong minimal pair in the computably enumerable (c.e.) Turing degrees, i.e. a pair of nonzero c.e. degrees a and b such that a∩b = 0 and for any nonzero c.e. degree x ≤ a, b ∪ x ≥ a.

Publisher

World Scientific Pub Co Pte Lt

Subject

Logic

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219061315500038

Reference17 articles.

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4. Lower Bounds for Pairs of Recursively Enumerable Degrees

5. A recursively enumerable degree which will not split over all lesser ones

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