Determinacy in strong cardinal models

We give limits defined in terms of abstract pointclasses of the amount of determinacy available in certain canonical inner models involving strong cardinals. We show for example: Theorem A Det(Π1 1-IND)⇒there exists an inner model with a strong cardinal. Theorem B Det(AQI) ⇒there exist type-1 mice and hence inner models with proper classes of strong cardinals where Π1 1-IND (AQI) is the pointclass of boldface Π1 1-inductive (respectively arithmetically quasi-inductive) sets of reals.

• Type: Journal
• Year: 2011
• Where: JSYML
• Authors: Philip D. Welch
• Keywords: Aqi, Inductive Sets, Inner Models, JSYML 2011