TY - JOUR
T1 - On successors of singular cardinals
AU - Shelah, Saharon
PY - 1979/1/1
Y1 - 1979/1/1
N2 - This chapter discusses the successors of singular cardinals and explains the situation for the successor of a strong limit singular cardinal λ. The chapter finds a special subset S* (λ+), from which the stationary subsets of λ+ can be found, which can be stopped from being stationary by μ-complete forcing. If λ is a singular strong limit, then for every normal two place function d from λ+ to κ = cfλ, So (d)≡ Sl (d) ∪ CF(λ+,≤ κ) ≡ λ+ - S* ( λ+) modDλ+. Therefore, So (d) does not depend on d up to equivalence modDλ+.
AB - This chapter discusses the successors of singular cardinals and explains the situation for the successor of a strong limit singular cardinal λ. The chapter finds a special subset S* (λ+), from which the stationary subsets of λ+ can be found, which can be stopped from being stationary by μ-complete forcing. If λ is a singular strong limit, then for every normal two place function d from λ+ to κ = cfλ, So (d)≡ Sl (d) ∪ CF(λ+,≤ κ) ≡ λ+ - S* ( λ+) modDλ+. Therefore, So (d) does not depend on d up to equivalence modDλ+.
UR - http://www.scopus.com/inward/record.url?scp=77951178997&partnerID=8YFLogxK
U2 - 10.1016/S0049-237X(08)71635-5
DO - 10.1016/S0049-237X(08)71635-5
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AN - SCOPUS:77951178997
SN - 0049-237X
VL - 97
SP - 357
EP - 380
JO - Studies in Logic and the Foundations of Mathematics
JF - Studies in Logic and the Foundations of Mathematics
IS - C
ER -