36 research outputs found
Martin's maximum and the non-stationary ideal
We analyze the non-stationary ideal and the club filter at aleph_1 under MM
Combinatorial Properties and Dependent choice in symmetric extensions based on L\'{e}vy Collapse
We work with symmetric extensions based on L\'{e}vy Collapse and extend a few
results of Arthur Apter. We prove a conjecture of Ioanna Dimitriou from her
P.h.d. thesis. We also observe that if is a model of ZFC, then
can be preserved in the symmetric extension of in terms of
symmetric system , if
is -distributive and is -complete.
Further we observe that if is a model of ZF + , then
can be preserved in the symmetric extension of in terms of
symmetric system , if
is -strategically closed and is
-complete.Comment: Revised versio
-Clubs of : Paradise in heaven
Let be three infinite cardinals, the first two being
regular. We show that if there is no inner model with large cardinals, is regular, where denotes the least
size of a cofinal subset in , and cf, then (a) the -club filters on and
are isomorphic, and (b) the ideal dual to the
-club filter on (and hence the restriction of the
nonstationary ideal on to sets of uniform cofinality
) is not --saturated