An infinite cardinal λ is Magidor if and only if (Formula presented.). It is known that if λ is Magidor then (Formula presented.) for some α < λ, and the first such α is denoted by α m (λ). In this paper we try to understand some of the properties of α m (λ). We prove that α m (λ) can be the successor of a supercompact cardinal, when λ is a Magidor cardinal. From this result we obtain the consistency of α m (λ) being a successor of a singular cardinal with uncountable cofinality.
Bibliographical noteFunding Information:
Acknowledgements First author’s research is supported by Shelah’s ERC grant 338821. We should like to thank the anonymous referee for many helpful suggestions that improved this paper’s readability and correctness.
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim