| Popis: |
We study determinacy from the perspective of inner model theory. In this thesis, there are three main results and all of them claim that there is a model of some strong determinacy axiom. Firstly, we show that if V is self-iterable and has inaccessible limit of Woodin cardinals, then its derived model satisfies "ADℝ+θ is regular." Secondly, we show that AD holds in the Chang model assuming the existence of an lbr hod pair with a Woodin limit of Woodin cardinals. Lastly, we introduce a new determinacy axiom called "ADℝ+θ is a strong cardinal'' and show its consistency. |
