Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 20 February 2019, 17:00 hrs

Room: S17#04-06, Department of Mathematics, NUS

Speaker: Liu Yong.

Title: There is no strong minimal pair.

URL: http://www.comp.nus.edu.sg/~fstephan/logicseminar.html

Abstract:

A strong minimal pair in r.e. degrees is defined to be a pair of

A, B such that they are incomparable and for any non-recursive r.e. set W

below A, B+W computes A. Historically, this was a difficult problem.

Slaman showed a weaker version of this (i.e. B+W computes a third set C,

instead of A), and it is called Slaman-Triple nowadays. Only recently,

people showed that there is a strong minimal pair. However, we realized

that there is a problem in that paper. Then we turned the problem into a

proof that there is no strong minimal pair. In this talk, we will sketch

the proof.