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arXiv · 1304.3955

On rapid idempotent ultrafilters

Peter Krautzberger
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Abstract

This short note contains the proofs of two small but somewhat surprising results about ultrafilters on $\mathbb{N}$: 1. strongly summable ultrafilters are rapid, 2. every rapid ultrafilter induces a closed left ideal of rapid ultrafilters. As a consequence, there will be rapid minimal idempotents in all models of set theory with rapid ultrafilters.

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Peter Krautzberger. 2013-05-05. On rapid idempotent ultrafilters. https://arxiv.org/abs/1304.3955

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