It is proved that a strong instance of the guessing principle ♣AD on the first uncountable cardinal follows from either the principle [InlineEquation not available: see fulltext.], 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 ℵ1 .
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- Club AD
- Dowker space
- Luzin set
- Strongly unbounded coloring