TY - JOUR
T1 - Representing sets of ordinals as countable unions of sets in the core model
AU - Magidor, Menachem
PY - 1990/1
Y1 - 1990/1
N2 - We prove the following theorems.Theorem 1.(¬0#).Every set of ordinals which is closed under primitive recursive set functions is a countable union of sets in L. Theorem 2.(No inner model with an Erdös cardinal, i.e.k→(ω1)<ω.)For every ordinal β, there is in K an algebra on β with countably many operationssuch that every subset of β closed under the operations of the algebra is acountable union of sets in K.
AB - We prove the following theorems.Theorem 1.(¬0#).Every set of ordinals which is closed under primitive recursive set functions is a countable union of sets in L. Theorem 2.(No inner model with an Erdös cardinal, i.e.k→(ω1)<ω.)For every ordinal β, there is in K an algebra on β with countably many operationssuch that every subset of β closed under the operations of the algebra is acountable union of sets in K.
UR - http://www.scopus.com/inward/record.url?scp=0040108145&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1990-0939805-5
DO - 10.1090/S0002-9947-1990-0939805-5
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AN - SCOPUS:0040108145
SN - 0002-9947
VL - 317
SP - 91
EP - 126
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 1
ER -