## 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

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