A Minimal Pair in the Quotient Structure M/NCup

Authors:
Rongfang Bie;Guohua Wu
Affiliations:
School of Information Science and Technology, Beijing Normal University, Beijing 100875, People's Republic of China;Division of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 639798, Republic of Singapore
Venue:
CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
Year:
2007

Citing 4
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Abstract

In this paper, we prove the existence of a minimal pair of c.e.degrees a and b such that both of them are cuppable, and noincomplete c.e. degree can cup both of them to 0'. As aconsequence, [a] and [b] form a minimal pair inM/NCup, the quotient structure of the cappabledegrees modulo noncuppable degrees. We also prove that the dual ofLempp's conjecture is true.