Inner models with many Woodin cardinals
This paper extends the author's work on fine structure and iteration trees [see the review above] to models with more than one Woodin cardinal. The main result of the paper is: Assume there are (in order type) \(\theta\)-many Woodin cardinals. Then there is a good extender sequence \(\vec E\) such that (1) \(L[\vec E]\models\) ``there are \(\theta\) Woodin cardinals'', (2) every level \(J^{\vec E}_ \alpha\) of \(L[\vec E]\) is an \(\omega\)-sound, meek premouse, (3) \(L[\vec E]\models\text{GCH}\). The paper concludes with a discussion of minimal models which also satisfy ``there are \(\omega\) Woodin cardinals''. The paper announces results to appear elsewhere of the case where there are \(n\) Woodin cardinals.
models with more than one Woodin cardinal
scientific article; zbMATH DE number 503599