Frank Stephan: Computational aspects of the hyperimmune-free degrees

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.

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