Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 15 August 2018, 17:00 hrs

Room: S17#04-05, Department of Mathematics, NUS

Speaker: Frank Stephan

Title: Computational aspects of the hyperimmune-free degrees

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

A set A has hyperimmune-free degree, if every set B

Turing equivalent to A is already truth-table equivalent to A.

Equivalently, one can also say that every function f Turing reducible

to A is majorised by a recursive function.

Starting with a result that there is a recursive tree T

with uncountably many infinite branches such that all of these

have hyperimmune-free degree, the authors (Ng Keng Meng, Frank Stephan,

Yang Yue and Yu Liang) investigated the overall notion of hyperimmune-free

degrees, their jumps and in particular the extent to which one can

strengthen the before-mentioned result. Indeed, one can achieve that

all the infinite branches on the tree T are not only

hyperimmune-free but also jump-traceable, Schnorr trivial and

of either minimal or recursive Turing degree.