7 research outputs found
Computably enumerable Turing degrees and the meet property
Working in the Turing degree structure, we show that those degrees which contain computably enumerable sets all satisfy the meet property, i.e. if a is c.e. and b < a, then there exists non-zero m < a with b ^m = 0. In fact, more than this is true: m may always be chosen to be a minimal degree. This settles a conjecture of Cooper and Epstein from the 80s
There are no maximal d.c.e. wtt-degrees
В статье доказывается, что не существует максимальной 2-в.п. wtt-степени в 2-в.п. wtt-степеня
Structural properties of the local Turing degrees
In this thesis we look at some properties of the local Turing Degrees, as a partial
order. We first give discussion of the Turing Degrees and certain historical results,
some translated into a form resembling the constructions we look at later.
Chapter 1 gives a introduction to the Turing Degrees, Chapter 2 introduces the
Local Degrees. In Chapter 3 we look at minimal Turing Degrees, modifying some
historical results to use a priority tree, which we use in chapter 4 to prove the new
result that every c.e. degree has the (minimal) meet property. Chapter 5 uses
similar methods to establish existence of a high 2 degree that does not have the meet
property