On the non-extendibility of strongness and supercompactness through strong compactness

Volume 174 / 2002

Arthur W. Apter Fundamenta Mathematicae 174 (2002), 87-96 MSC: 03E35, 03E55. DOI: 10.4064/fm174-1-5


If $\kappa $ is either supercompact or strong and $\delta < \kappa $ is $\alpha $ strong or $\alpha $ supercompact for every $\alpha < \kappa $, then it is known $\delta $ must be (fully) strong or supercompact. We show this is not necessarily the case if $\kappa $ is strongly compact.


  • Arthur W. ApterDepartment of Mathematics
    Baruch College of CUNY
    New York, NY 10010, U.S.A.

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