A new small Dowker space

It is proved that a strong instance of the guessing principle ♣ AD on the first uncountable cardinal follows from either the principle , or the principle ♢ ( b ) , or the existence of a Luzin set. In particular, any of the above hypotheses entails the existence of a Dowker space of size ℵ 1 .

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Bibliographic Details
Published in:Periodica mathematica Hungarica 2024-03, Vol.88 (1), p.102-117
Main Authors: Rinot, Assaf, Shalev, Roy, Todorcevic, Stevo
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Principles
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Summary:It is proved that a strong instance of the guessing principle ♣ AD on the first uncountable cardinal follows from either the principle , or the principle ♢ ( b ) , or the existence of a Luzin set. In particular, any of the above hypotheses entails the existence of a Dowker space of size ℵ 1 .
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-023-00541-6