Premium
Generalized Prikry forcing and iteration of generic ultrapowers
Author(s) -
Sakai Hiroshi
Publication year - 2005
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.200410047
Subject(s) - forcing (mathematics) , mathematics , sequence (biology) , ultrafilter , relation (database) , combinatorics , discrete mathematics , mathematical analysis , computer science , chemistry , biochemistry , database
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 n , j m,n | m ≤ n ≤ ω 〉 is the iteration of ultrapowers of V by U , then the sequence of critical points 〈 j 0, n ( κ ) | n ∈ ω 〉 is a Prikry generic sequence over M ω . In this paper we generalize this for normal precipitous filters. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)