TY - JOUR
T1 - Covering the Baire space by families which are not finitely dominating
AU - Mildenberger, Heike
AU - Shelah, Saharon
AU - Tsaban, Boaz
PY - 2006/7
Y1 - 2006/7
N2 - It is consistent (relative to ZFC) that each union of max {b,g} many families in the Baire space ωω which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of the reduced ultrapower ωω/U is greater than max{b,g}. The model is constructed by oracle chain condition forcing, to which we give a self-contained introduction.
AB - It is consistent (relative to ZFC) that each union of max {b,g} many families in the Baire space ωω which are not finitely dominating is not dominating. In particular, it is consistent that for each nonprincipal ultrafilter U, the cofinality of the reduced ultrapower ωω/U is greater than max{b,g}. The model is constructed by oracle chain condition forcing, to which we give a self-contained introduction.
KW - Cofinality of ultrapowers
KW - Finitely dominating families
KW - Groupwise density number g
KW - Unbounding number b
UR - http://www.scopus.com/inward/record.url?scp=33646035824&partnerID=8YFLogxK
U2 - 10.1016/j.apal.2005.09.008
DO - 10.1016/j.apal.2005.09.008
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AN - SCOPUS:33646035824
SN - 0168-0072
VL - 140
SP - 60
EP - 71
JO - Annals of Pure and Applied Logic
JF - Annals of Pure and Applied Logic
IS - 1-3
ER -