Infinite decreasing chains in the Mitchell order
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Publication:6324263
DOI10.1007/S00153-021-00762-XarXiv1908.10224MaRDI QIDQ6324263
Publication date: 27 August 2019
Abstract: It is known that the behavior of the Mitchell order substantially changes at the level of rank-to-rank extenders, as it ceases to be well-founded. While the possible partial order structure of the Mitchell order below rank-to-rank extenders is considered to be well understood, little is known about the structure in the ill-founded case. The purpose of the paper is to make a first step in understanding this case, by studying the extent to which the Mitchell order can be ill-founded. Our main results are (i) in the presence of a rank-to-rank extender there is a transitive Mitchell order decreasing sequence of extenders of any countable length, and (ii) there is no such sequence of length .
Consistency and independence results (03E35) Large cardinals (03E55) Other classical set theory (including functions, relations, and set algebra) (03E20)
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