The Journal of Symbolic Logic

Research Article

The weak □* is really weaker than the full □

Shai Ben-Davida1 and Menachem Magidora2

a1 Department of Mathematics, University of Toronto, Toronto, Ontario M5S 1A4, Canada

a2 Department of Mathematics, The Hebrew University, Jerusalem, Israel

Abstract

We show that relative to the consistency of a supercompact cardinal does not imply . The model-theoretic transfer property ⟨ℵ1, ℵ0⟩ → ⟨ℵ ω + 1, ℵ ω ⟩ does not imply , and it is consistent to have an ultrafilter on ℵ ω + 1 which is λ-indecomposible for all ω < λ < ℵ ω .

(Received November 29 1984)

(Revised February 18 1986)