DOWKER AND SUPER-DOWKER FILTERS

作者：Cummings James^*; Morgan Charles

来源：PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 145(12): 5381-5390.

DOI：10.1090/proc/13706

• Dowker filter
• super-Dowker filter
• supercompact cardinal
• forcing

Our main results show that a very simple forcing construction can be used to add Dowker and super-Dowker filters:
Let kappa be uncountable with kappa(<kappa) = kappa. Let G be generic over V for Add(kappa, kappa(++)). Then in V [G] there is a Dowker filter on kappa(+).
Let V be Laver's model in which kappa is supercompact and the supercompactness of kappa is indestructible under kappa-directed closed forcing, and let G be generic for Add(kappa, kappa(++)). Then in V [G] there is a super-Dowker filter on kappa(+).

• 出版日期2017-12