Diamonds, Compactness, and Measure Sequences

Published 3 May 2017 in math.LO | (1705.01611v2)

Abstract: We establish the consistency of the failure of the diamond principle on a cardinal $\kappa$ which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of $\kappa$ in a Radin generic extension.

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Omer Ben-Neria

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