## Abstract

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.

Original language | American English |
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Pages (from-to) | 95-104 |

Number of pages | 10 |

Journal | Mathematical Logic Quarterly |

Volume | 65 |

Issue number | 1 |

DOIs | |

State | Published - May 2019 |

### Bibliographical note

Funding 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.

Publisher Copyright:

© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim