Thursday, 31 January 2018, 15:30, Sala Verde.

Dávid Natingga (University of Leeds)

*Introduction to α-Computability Theory*

An ordinal α is admissible iff the α-th level L

_{α}of Gödel’s constructible hierarchy satisfies the axioms of Kripke-Platek set theory (roughly predicative part of ZFC).α-computability theory is the study of the first-order definability theory over Gödel’s L

_{α}for an admissible ordinal α.Equivalently, α-computability theory studies the computability on a Turing machine with a transfinite tape and time of an order type α for an admissible ordinal α.

The field of α-computability theory is the source of deep connections between computability theory, set theory, model theory, definability theory and other areas of mathematics.