TY - JOUR
T1 - The first omitting cardinal for Magidority
AU - Garti, Shimon
AU - Hayut, Yair
N1 - Publisher Copyright:
© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2019/5
Y1 - 2019/5
N2 - An infinite cardinal λ is Magidor if and only if (Formula presented.). It is known that if λ is Magidor then (Formula presented.) for some α < λ, and the first such α is denoted by α m (λ). In this paper we try to understand some of the properties of α m (λ). We prove that α m (λ) can be the successor of a supercompact cardinal, when λ is a Magidor cardinal. From this result we obtain the consistency of α m (λ) being a successor of a singular cardinal with uncountable cofinality.
AB - An infinite cardinal λ is Magidor if and only if (Formula presented.). It is known that if λ is Magidor then (Formula presented.) for some α < λ, and the first such α is denoted by α m (λ). In this paper we try to understand some of the properties of α m (λ). We prove that α m (λ) can be the successor of a supercompact cardinal, when λ is a Magidor cardinal. From this result we obtain the consistency of α m (λ) being a successor of a singular cardinal with uncountable cofinality.
UR - http://www.scopus.com/inward/record.url?scp=85065312431&partnerID=8YFLogxK
U2 - 10.1002/malq.201800026
DO - 10.1002/malq.201800026
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:85065312431
SN - 0942-5616
VL - 65
SP - 95
EP - 104
JO - Mathematical Logic Quarterly
JF - Mathematical Logic Quarterly
IS - 1
ER -