Ivan Soskov (Sofia)
Definability Properties of Marker's Extensions

The Marker's extensions of a structure are introduced by Goncharov and Khoussainov in 2002. The definition is based on earlier work of Marker. We shall discuss results on definability in Marker's extensions and prove that for every finite ordinal n, the (n+1)-th Marker's extension of a countable structure A behaves as a Model Theoretic n-th jump inversion of A⊕∅(n). We shall show that in the general case such kind of jump inversions are impossible for infinite recursive ordinals.