Generic left-separated spaces and calibers

by Juhasz and Shelah. [JuSh:795]
Topology and its Applications, 2003
We use a natural forcing to construct a left-separated topology on an arbitrary cardinal kappa . The resulting left-separated space X_kappa is also 0-dimensional T_2, hereditarily Lindel{o}f, and countably tight. Moreover if kappa is regular then d(X_kappa)= kappa, hence kappa is not a caliber of X_kappa, while all other uncountable regular cardinals are. We also prove it consistent that for every countable set A of uncountable regular cardinals there is a hereditarily Lindel{o}f T_3 space X such that varrho =cf(varrho) > omega is a caliber of X exactly if varrho not in A .

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