Which pairs of cardinals can be Hartogs and Lindenbaum numbers of a set?
Volume 267 / 2024
Fundamenta Mathematicae 267 (2024), 231-241
MSC: Primary 03E25; Secondary 03E35
DOI: 10.4064/fm231006-14-8
Published online: 7 November 2024
Abstract
Given any , we construct a symmetric extension in which there is a set X such that \aleph (X)=\lambda and \aleph ^*(X)=\kappa . Consequently, we show that \mathsf{ZF} {}+{}“for all pairs of infinite cardinals \lambda \leq \kappa there is a set X such that \aleph (X)=\lambda \leq \kappa =\aleph ^*(X)” is consistent.
