TY - JOUR
T1 - Approachability at the second successor of a singular cardinal
AU - Gitik, Moti
AU - Krueger, John
PY - 2009/12
Y1 - 2009/12
N2 - We prove that if μ is a regular cardinal and ℙ is a μ-centered forcing poset, then ℙ forces that (I[μ++])v generates I[μ++] modulo clubs. Using this result, we construct models in which the approachability property fails at me successor of a singular cardinal. We also construct models in which the properties of being internally club and internally approachable are distinct for sets of size the successor of a singular cardinal.
AB - We prove that if μ is a regular cardinal and ℙ is a μ-centered forcing poset, then ℙ forces that (I[μ++])v generates I[μ++] modulo clubs. Using this result, we construct models in which the approachability property fails at me successor of a singular cardinal. We also construct models in which the properties of being internally club and internally approachable are distinct for sets of size the successor of a singular cardinal.
KW - Approachability ideal
KW - Internally approachable
UR - http://www.scopus.com/inward/record.url?scp=74349106822&partnerID=8YFLogxK
U2 - 10.2178/jsl/1254748688
DO - 10.2178/jsl/1254748688
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AN - SCOPUS:74349106822
SN - 0022-4812
VL - 74
SP - 1211
EP - 1224
JO - Journal of Symbolic Logic
JF - Journal of Symbolic Logic
IS - 4
ER -