Arhangelskii and Buzyakova proved that the cardinality of a first countable linearly Lindelxf6;f space does not exceed 20. Consequently, a first countable linearly Lindelxf6;f space is Lindelxf6;f if ω>20. They asked whether every linearly Lindelxf6;f first countable space is Lindelxf6;f in ZFC. This question is supported by the fact that all known linearly Lindelxf6;f not Lindelxf6;f spaces are of character at least ω. We answer this question in the negative by constructing a counterexample from MA+ω<20.
A modification of Alsters Michael space that is first countable is presented.