×

zbMATH — the first resource for mathematics

Inner models with many Woodin cardinals. (English) Zbl 0805.03043
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.

MSC:
03E55 Large cardinals
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] D.A. Martin and J.R. Steel, Iteration trees, in the J. AMS, to appear · Zbl 0808.03035
[2] J.R. Steel, Projectively wellordered inner models, to appear
[3] W.J. Mitchell, Embeddings of iteation trees, unpublished notes
[4] W.J. Mitchell and J.R. Steel, Fine structure and iteration trees, ASL Lecture Notes in Logic, to appear
[5] Schimmerling, E., Combinatorial principles in the core model, Ph.D. thesis, (1992), UCLA
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.