Some results on Specker’s problem

Arthur W. Apter, Moti Gitik

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)227-249
Number of pages23
JournalPacific Journal of Mathematics
Issue number2
StatePublished - Oct 1988


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