2011 seminar talk: Definability in the enumeration degrees
Talk held by Mariya Soskova (Sofia University, Bulgaria) at the KGRC seminar on 2011-05-19.
I will talk about a joint project with H. Ganchev, whose aim is to study the definability properties, of the local structure of the enumeration degrees. We start by studying K-pairs of enumeration degrees, a notion introduced by Kalimullin. We show that the class of K-pairs are first order definable in the local structure. Using this result, we show that the local structure of the Turing degrees (the Delta-two Turing degrees) has a first order definable isomorphic copy in the local structure of the enumeration degrees.