On the cardinality of separable pseudoradial spaces

The aim of this paper is to consider questions concerning the possible maximum cardinality various separable pseudoradial (in short: SP) spaces. most intriguing question here if there in ZFC a regular (or just Hausdorff) SP space >c. While left open, we establish number non-trivial results that list below. It consistent with MA+c=ℵ2 countably tight and compact 2c. If κ measurable cardinal then forcing extension obtained by adding many Cohen reals, every has at c. κ>ℵ1 reals are added model GCH pseudocompact countable dense set isolated points c≤ℵ2 0-dimensional greater than