Please add the example of an uncountable, first countable, Hausdorff, Lindelöf scattered space!

[jibnew]

Yesterday, answering the question "Example of an uncountable scattered space with some properties" on mathoverflow, Taras Banakh constructed an uncountable, first countable, Hausdorff, Lindelöf scattered space. I believe this must necessarily be on the π-base!

[StevenClontz]

A known deficiency of the database is that we currently have no way to distinguish when assertions are made assuming axioms beyond ZFC. So since this result is independent of ZFC, we cannot (yet) include it.

Leaving this open for the day we can do so, however.

[jibnew]

A known deficiency of the database is that we currently have no way to distinguish when assertions are made assuming axioms beyond ZFC. So since this result is independent of ZFC, we cannot (yet) include it.

Leaving this open for the day we can do so, however.

Actually yesterday Will Brian came up with another example, in ZFC :)

[StevenClontz]

Ah, classic Will. :)