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## Bulletin of the Polish Academy of Sciences. Mathematics

2009 | 57 | 3 | 189-197
Tytuł artykułu

### Sandwiching the Consistency Strength of Two Global Choiceless Cardinal Patterns

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EN
Abstrakty
EN
We provide upper and lower bounds in consistency strength for the theories "ZF + $¬AC_ω$ + 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 ω" and "ZF + $¬AC_ω$ + 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 ω₁". In particular, our models for both of these theories satisfy "ZF + $¬AC_ω$ + κ is singular iff κ is either an uncountable limit cardinal or the successor of an uncountable limit cardinal".
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Rocznik
Tom
Numer
Strony
189-197
Opis fizyczny
Daty
wydano
2009
Twórcy
autor
• Department of Mathematics, Baruch College of CUNY, New York, NY 10010, U.S.A.
• The CUNY Graduate Center, Mathematics, 365 Fifth Avenue, New York, NY 10016, U.S.A.
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