Generalized Prikry forcing and iteration of generic ultrapowers.

Authors :: Sakai, Hiroshi
Source :: Mathematical Logic Quarterly; Sep2005, Vol. 51 Issue 5, p507-523, 17p
Publication Year :: 2005
Abstract: It is known that there is a close relation between Prikry forcing and the iteration of ultrapowers: If U is a normal ultrafilter on a measurable cardinal κ and 〈M<subscript>n</subscript>, j<subscript>m,n</subscript> | m ≤ n ≤ ω〉 is the iteration of ultrapowers of V by U, then the sequence of critical points 〈j<subscript>0,n</subscript>(κ) | n ∈ ω〉 is a Prikry generic sequence over M<subscript>ω</subscript>. In this paper we generalize this for normal precipitous filters. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]