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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Definable singularity


Author: William J. Mitchell
Journal: Trans. Amer. Math. Soc. 327 (1991), 407-426
MSC: Primary 03E45; Secondary 03E55
DOI: https://doi.org/10.1090/S0002-9947-1991-1036006-0
MathSciNet review: 1036006
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Abstract: The main result of this paper is a characterization of singular cardinals in terms of the core model, assuming that there is no model of $ \exists \kappa \,o(\kappa)= {\kappa ^{ + + }}$. This characterization is used to prove a result in infinitary Ramsey theory. In the course of the proof we develop a simplified statement of the covering lemma for sequences of measures which avoids the use of mice. We believe that this development will be capable of isolating almost all applications of the covering lemma from the detailed structure of the core model.


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DOI: https://doi.org/10.1090/S0002-9947-1991-1036006-0
Keywords: Singular cardinals, core model, covering lemma
Article copyright: © Copyright 1991 American Mathematical Society