Introduction to alpha-Computability Theory

24 January 2019
Versione stampabile

Venue: PovoZero, via Sommarive, 14 - Povo - Sala Seminari "-1"
Time: 2:30

Speaker:

  • Dávid Natingga, PhD candidate - University of Leeds

Abstract:
An ordinal alpha is admissible iff alpha-th level L_alpha of Goedel's constructible hierarchy satisfies the axioms of Kripke-Platek set theory (roughly predicative part of ZFC).  Alpha-computability theory is the study of the first-order definability theory over Goedel's L_alpha for an admissible ordinal alpha.

Equivalently, alpha-computability theory studies the computability on a Turing machine with a transfinite tape and time of an order type alpha for an admissible ordinal alpha. The field of alpha-computability theory is the source of deep connections between computability theory, set theory, model theory, definability theory and other areas of mathematics.

In the seminar I will assume basic familiarity with computability theory and axiomatic set theory. Other notions such as Goedel's constructible hierarchy and an admissible ordinal will be explained.

Contact person:  Roberto Zunino