A ZFC Dowker space in aleph_(ω+1): an application of pcf theory to topology
classification
🧮 math.LO
keywords
spacedowkeralephomegaprooftheoryapplicationbound
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A ZFC Dowker space is constructed which has cardinality $\aleph_{\omega+1}$. This provides a bound in ZFC to the first cardinal in which there is a ZFC Dowker space. The space we construct is a closed and cofinal subspace of M.~E.~Rudin's Dowker space from 1971. A theorem from pcf theory used in the proof, but otherwise the proof is elementary.
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