Logic & Set Theory Seminar: The Ramified Analytical Hierarchy and Strong Logics
Philip Welch, University of Bristol
Howard House 4th Floor Seminar Room
The ramified analytical hierarchy defined by Kleene builds up a hierarchy of models of subsystems of analysis in a second order definable manner.
We address a question of Kennedy as to what can be done using strong logics to re-define the stages of Kleene's hierarchy, in the spirit of "Inner Models from Extended Logics" of Kennedy, Magidor, & Väänänen. In this paper they followed a suggestion of Gödel that the definability function used to build the levels of the constructible hierarchy be modified to make use of stronger logics. The resultant hierarchy might, or might not, then be L itself. We show that by changing the logic in the ramified analytical hierarchy allows one to comstruct, eg., the minimal 'correct' model of analysis.