Abstract
The Proper Forcing Axiom implies that compact Hausdorff spaces are either first-countable or contain a converging \(\omega_1\)-sequence.
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Dow, A., Hart, K.P. PFA and \(\omega_1\)-free compact spaces. Acta Math. Hungar. 166, 57–64 (2022). https://doi.org/10.1007/s10474-021-01197-9
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DOI: https://doi.org/10.1007/s10474-021-01197-9