TY - JOUR
T1 - On the existence of nonregular ultrafilters and the cardinality of ultrapowers
AU - Magidor, M.
PY - 1979/4
Y1 - 1979/4
N2 - Assuming the consistency of huge cardinals, we prove that ω3 can carry an ultrafilter D such that ω1ω3/D has cardinality ω3. (Hence D is not (ω3, ω1) regular.) Similarly ω2 can carry an ultrafilter D such that ωω2/D has cardinality ω2. (Hence D is not (ω2, ω) regular).
AB - Assuming the consistency of huge cardinals, we prove that ω3 can carry an ultrafilter D such that ω1ω3/D has cardinality ω3. (Hence D is not (ω3, ω1) regular.) Similarly ω2 can carry an ultrafilter D such that ωω2/D has cardinality ω2. (Hence D is not (ω2, ω) regular).
KW - Huge cardinals
KW - Regular ultrafilter
KW - Ultrafilter
KW - Ultraproduct
UR - http://www.scopus.com/inward/record.url?scp=80054863924&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-1979-0526312-2
DO - 10.1090/S0002-9947-1979-0526312-2
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AN - SCOPUS:80054863924
SN - 0002-9947
VL - 249
SP - 97
EP - 111
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 1
ER -