The aim is to demonstrate that the Chang model satisfies certain determinacy properties under specific conditions.
Assumed the existence of a hod pair with a Woodin cardinal that is a limit of Woodin cardinals.
Analyzed the behavior of the Chang model under these conditions.
Explored the general characteristics of set generic extensions.
The Chang model satisfies 30AD+ in all set generic extensions.
Confirmed that specific configurations of Woodin cardinals lead to determinacy properties.
Provided foundational support for further studies on large cardinals and their implications.
Resumen
Assuming the existence of a certain hod pair with a Woodin cardinal that is a limit of Woodin cardinals, we show that the Chang model satisfies A D + AD^+ in all set generic extensions.