Measurable cardinals and the cardinality of Lindel"of spaces

If it is consistent that there is a measurable cardinal, then it is consistent that all points g-delta Rothberger spaces have “small” cardinality.

💡 Research Summary

The paper investigates the interplay between large‑cardinal hypotheses—specifically the existence of a measurable cardinal—and the cardinalities of certain topological spaces that satisfy strong selection principles. The author begins by recalling that a measurable cardinal κ carries a κ‑complete non‑principal ultrafilter, which can be used as a forcing notion to produce extensions of the universe in which many combinatorial properties are preserved while the continuum can be tightly controlled. By forcing with a κ‑complete ultrafilter, one can obtain a model V