Cofinality changes required for a large set of unapproachable ordinals below <IMG BORDER="0" SRC="/proc/2007-135-08/S0002-9939-07-08760-6/gif-title0/img1.gif" >期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Cofinality changes required for a large set of unapproachable ordinals below

Authors:	M. C. Stanley

Affiliation:	Mathematics Department, San Jose State University, San Jose, California 95192

Abstract:	In , assume that $aleph _{omega }$ is a strong limit cardinal and $2^{aleph _{omega }}=aleph _{omega +1}$ . Let be the set of approachable ordinals less than $aleph _{omega +1}$ . An open question of M. Foreman is whether can be non-stationary in some $aleph _{omega }$ and $aleph _{omega +1}$ preserving extension of . It is shown here that if is such an outer model, then ${{,k<omega :mathop{text{cf}}^{W}(aleph ^{V}_{k})=aleph ^{W}_{n},}}$ is infinite, for each positive integer .

Keywords:	Approachable ordinal $I[lambda ]$ cofinality ErdH os-Rado

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