TY - JOUR
T1 - 0# and Elementary end extensions of Vκ
AU - Leshem, Amir
PY - 2001
Y1 - 2001
N2 - In this paper we prove that if κ is a cardinal in L[0#], then there is an inner model M such that M (Vκ, ε) has no elementary end extension. In particular if 0# exists, then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than N1 of uncountable cofinality in L[0#] is Mahlo in every strict inner model of L[0#].
AB - In this paper we prove that if κ is a cardinal in L[0#], then there is an inner model M such that M (Vκ, ε) has no elementary end extension. In particular if 0# exists, then weak compactness is never downwards absolute. We complement the result with a lemma stating that any cardinal greater than N1 of uncountable cofinality in L[0#] is Mahlo in every strict inner model of L[0#].
KW - 0
KW - Inner models
KW - Models of set theory
UR - https://www.scopus.com/pages/publications/33646839790
U2 - 10.1090/s0002-9939-01-05847-6
DO - 10.1090/s0002-9939-01-05847-6
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AN - SCOPUS:33646839790
SN - 0002-9939
VL - 129
SP - 2445
EP - 2450
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 8
ER -