Open filters and measurable cardinals

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This paper shows the lattice structure of free open filters in scattered spaces, indicating implications for measurable cardinals.

The study shows that the poset of free open filters can be a lattice under certain space conditions.
For each natural number, a scattered space is constructed where the filters are order isomorphic to a chain.
Introducing a new stratification of ultrafilters elucidates properties related to measurable cardinals.
Establishing a connection between metric spaces and measurable cardinals may widen avenues for further theoretical exploration.

Bardyla et al. (2025) studied this question.

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