Some results on Specker’s problem

Arthur William Apter and Moti Gitik

Vol. 134 (1988), No. 2, 227–249

DOI: 10.2140/pjm.1988.134.227

Abstract

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 ℵ. In the second model, SP(ℵ) holds for every limit ℵ and for certain successor ℵ’s.

Mathematical Subject Classification 2000

Primary: 03E10

Secondary: 03E35, 03E55

Milestones

Received: 27 April 1987

Published: 1 October 1988