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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

The partition property for certain extendible measures on supercompact cardinals


Author: Donald H. Pelletier
Journal: Proc. Amer. Math. Soc. 81 (1981), 607-612
MSC: Primary 03E55; Secondary 04A10, 04A20
DOI: https://doi.org/10.1090/S0002-9939-1981-0601740-X
MathSciNet review: 601740
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Abstract: We give an alternate characterization of a combinatorial property of measures on $ {p_\kappa }\lambda $ introduced by Menas. We use this characterization to prove that if $ \kappa $ is supercompact, then all measures on $ {p_\kappa }\lambda $ in a certain class have the partition property. This result is applied to obtain a self-contained proof that if $ \kappa $ is supercompact and $ \lambda $ is the least measurable cardinal greater than $ \kappa $, then Solovay's "glue-together" measures on $ {p_\kappa }\lambda $ are not $ {2^\lambda }$-extendible.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0601740-X
Keywords: Supercompact cardinals, measures with the partition property, extendible measures, "glue-together" measures, restriction measures
Article copyright: © Copyright 1981 American Mathematical Society