TY - JOUR
T1 - Some results on Specker’s problem
AU - Apter, Arthur W.
AU - Gitik, Moti
PY - 1988/10
Y1 - 1988/10
N2 - Say that the Specker Property holds for a well ordered cardinal ℵ, and write this as SP(ℵ), if the power set of ℵ can be written as a countable union of sets of cardinality ℵ. Specker’s Problem asks whether it is possible to have a model in which SP(ℵ) holds for every ℵ. In this paper, we construct two models in which the Specker Property holds for a large class of cardinals. In the first model, SP(ℵ) holds for every successor K. In the second model, SP(ℵ) holds for every limit ℵ and for certain successor ℵ‘s.
AB - Say that the Specker Property holds for a well ordered cardinal ℵ, and write this as SP(ℵ), if the power set of ℵ can be written as a countable union of sets of cardinality ℵ. Specker’s Problem asks whether it is possible to have a model in which SP(ℵ) holds for every ℵ. In this paper, we construct two models in which the Specker Property holds for a large class of cardinals. In the first model, SP(ℵ) holds for every successor K. In the second model, SP(ℵ) holds for every limit ℵ and for certain successor ℵ‘s.
UR - http://www.scopus.com/inward/record.url?scp=84972554165&partnerID=8YFLogxK
U2 - 10.2140/pjm.1988.134.227
DO - 10.2140/pjm.1988.134.227
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AN - SCOPUS:84972554165
VL - 134
SP - 227
EP - 249
JO - Pacific Journal of Mathematics
JF - Pacific Journal of Mathematics
SN - 0030-8730
IS - 2
ER -