TY - JOUR
T1 - On power of singular cardinals
AU - Shelah, Saharon
PY - 1986/4
Y1 - 1986/4
N2 - Using elementary methods we find bounds for the function. Using only ZFC without additional assumptions, when e.g., is strong limit of uncountable confinality: (1) If there is no weakly inaccessible below (formula presented), then there is no such cardinal below (formula presented) (2) If (formula presented) is the first cardinal such that (formula presented) with (formula presented) then (formula presented) K when K is the first cardinal such that (formula presented) with cofinality (formula presented) We shall also reprove some of Galvin and Hajnafs results. We do not require any knowledge of earlier results on the subject.
AB - Using elementary methods we find bounds for the function. Using only ZFC without additional assumptions, when e.g., is strong limit of uncountable confinality: (1) If there is no weakly inaccessible below (formula presented), then there is no such cardinal below (formula presented) (2) If (formula presented) is the first cardinal such that (formula presented) with (formula presented) then (formula presented) K when K is the first cardinal such that (formula presented) with cofinality (formula presented) We shall also reprove some of Galvin and Hajnafs results. We do not require any knowledge of earlier results on the subject.
UR - http://www.scopus.com/inward/record.url?scp=84972541955&partnerID=8YFLogxK
U2 - 10.1305/ndjfl/1093636617
DO - 10.1305/ndjfl/1093636617
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AN - SCOPUS:84972541955
SN - 0029-4527
VL - 27
SP - 263
EP - 299
JO - Notre Dame Journal of Formal Logic
JF - Notre Dame Journal of Formal Logic
IS - 2
ER -