A model for global compactness

Joint work with Sittinon Jirattikansakul and Inbar Oren.

Abstract. In a classical paper by Ben-David and Magidor, a model of set theory was exhibited in which $\aleph_{\omega+1}$ carries a uniform ultrafilter that is $\theta$-indecomposable for every regular uncountable $\theta<\aleph_\omega$.

In this paper, we give a global version of this result, as follows:

Assuming the consistency of a supercompact cardinal, we produce a model of set theory in which for every singular cardinal $\lambda$, there exists a uniform ultrafilter on $\lambda^+$ that is $\theta$-indecomposable for every regular cardinal $\theta$ with $cf(\lambda)<\theta<\lambda$.

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