\(\Sigma_3^1\) absoluteness and the second uniform indiscernible
type: Item
instance of: scholarly article
title: \(\Sigma_3^1\) absoluteness and the second uniform indiscernible
zbMATH Open document ID: 0915.03042
DOI: 10.1007/BF02897063
author: K. Appert
published in: Israel Journal of Mathematics
publication date: 1999-06-27T00:00:00Z
review text: The authors prove that if \(r^\sharp\) exists for each real \(r\) and if \(\delta^{1}_{2}=\omega_{2}\), then there are inner models with strong cardinals. Also they prove that if the core model \(K\) is not \(\Sigma^{1}_{3}\)-absolute, there are inner models with strong cardinals. The authors' stated interest is in the construction of core models, and these hypotheses allow them to construct such models which contain large cardinals. This paper includes an extensive study of universal iterations, and it ends with suggested extensions and open questions.
reviewed by: J. M. Plotkin
Mathematics Subject Classification ID: 03E45
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 03E55
zbMATH DE Number: 1251447
zbMATH Keywords: inner models
zbMATH Keywords: strong cardinals
zbMATH Keywords: core model
zbMATH Keywords: universal iterations
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1251447