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The first measurable cardinal can be the first uncountable regular cardinal at any successor height
Author(s) -
Apter Arthur W.,
Dimitriou Ioanna M.,
Koepke Peter
Publication year - 2014
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201110007
Subject(s) - successor cardinal , uncountable set , regular cardinal , mathematics , cardinal number (linguistics) , combinatorics , philosophy , mathematical analysis , countable set , linguistics
We use techniques due to Moti Gitik to construct models in which for an arbitrary ordinal ϱ, ℵ ϱ + 1is both the least measurable and least regular uncountable cardinal.