Sandwiching the Consistency Strength of Two Global Choiceless Cardinal Patterns

Tom 57 / 2009

Arthur W. Apter Bulletin Polish Acad. Sci. Math. 57 (2009), 189-197 MSC: 03E25, 03E35, 03E45, 03E55. DOI: 10.4064/ba57-3-1

Streszczenie

We provide upper and lower bounds in consistency strength for the theories “ZF + $\neg $AC$_\omega $ + All successor cardinals except successors of uncountable limit cardinals are regular $+$ Every uncountable limit cardinal is singular $+$ The successor of every uncountable limit cardinal is singular of cofinality $\omega $” and “ZF + $\neg$AC$_\omega $ + All successor cardinals except successors of uncountable limit cardinals are regular $+$ Every uncountable limit cardinal is singular $+$ The successor of every uncountable limit cardinal is singular of cofinality $\omega _1$”. In particular, our models for both of these theories satisfy “ZF + $\neg$AC$_\omega $ + $\kappa $ is singular if{f} $\kappa $ is either an uncountable limit cardinal or the successor of an uncountable limit cardinal”.

Autorzy

  • Arthur W. ApterDepartment of Mathematics
    Baruch College of CUNY
    New York, NY 10010, U.S.A.
    and
    The CUNY Graduate Center, Mathematics
    365 Fifth Avenue
    New York, NY 10016, U.S.A.
    e-mail

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