Sesión ordinaria del Seminario (23-5-2012)

Fecha / Date: 23-5-2012.

Hora / Time: 10:30 h.

Lugar / Location: Seminario del módulo H1 del Departamento de Ciencias de la Computación e Inteligencia Artificial, Escuela Técnica Superior de Ingeniería Informática - Universidad de Sevilla.

Ponente / Lecturer: David Fernández Duque.

Título / Tittle: An arithmetic interpretation of transfinite provability logic.

Resumen / Abstract:
The provability logic GLP extend's Gödel's idea of considering the modal [] as a provability operator, by adding one modality [n] for each natural number n. These are then interpreted as provability in theories of increasing strength. We consider a further extension, GLP(X), where X is an ordinal parameter. In this talk, we shall present a possible interpretation of the operator [x] as "provable with omega-rules of nesting depth x", and show that soundness of GLP holds for this interpretation. Time permitting, we will discuss completeness as well.