\(\Sigma_3^1\) absoluteness and the second uniform indiscernible
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.
scientific article; zbMATH DE number 1251447
scientific article