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 Lα 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 Lα 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.