Inner models with many Woodin cardinals
type: Item
instance of: scholarly article
title: Inner models with many Woodin cardinals
zbMATH Open document ID: 0805.03043
DOI: 10.1016/0168-0072(93)90037-E
author: John Steel
published in: Annals of Pure and Applied Logic
publication date: 1994-03-07T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 03E55
zbMATH DE Number: 503599
zbMATH Keywords: fine structure
zbMATH Keywords: iteration trees
zbMATH Keywords: models with more than one Woodin cardinal
zbMATH Keywords: extender sequence
zbMATH Keywords: minimal models
MaRDI profile type: Publication
cites work: Iteration Trees
full work available at URL: 0168-0072(93)90037-e
OpenAlex ID: W2007638330
description: scientific article; zbMATH DE number 503599