Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 17 September 2014, 17:00 hrs

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

Speaker: Yang Yue

Title: On a Question of Cholak and Downey

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

In a paper entitled “On the Cantor-Bendixon rank of recursively

enumerable sets” (JSL 1993), Cholak and Downey showed that for every

recursive ordinal alpha and every nonrecursive r.e. degree d,

there is an r.e. set of rank alpha and degree d.

They also asked if one can generalize the result to

Delta-0-2 degrees, i.e., for every recursive

ordinal alpha and every nonrecursive Delta-0-2

degree d there is a Delta-0-2 set of rank

alpha and degree d. I will show the answer is positive.

This is a joint work with Rod Downey and Guohua Wu.