Computability Learning Seminar

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

"A Jump Inversion Theorem for Structures"

Given a structure $\mathcal{A}$, we defined last week another structure $\mathcal{A}'$  which we called the jump of $\mathcal{A}$. We know that for a Turing degree $\mathbf{d}\geq_T \mathbf{0}'$, there exists a degree $\mathbf{c}$ such that $\mathbf{c}'\equiv_T\mathbf{d}$ (Friedberg's jump inversion theorem), we will prove a similar theorem for structures by Soskova and Stukachev. Their theorem says that: For every structure $\mathcal{A}$ which codes $\vec{\mathbf{0}}'$, there is a structure $\mathcal{C}$ whose jump is effectively bi-interpretable with $\mathcal{A}$.

MC 5413