Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Bulletin of the Polish Academy of Sciences. Mathematics

2009 | 57 | 3 | 189-197

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

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".

189-197

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.