The theory of filter spaces is introduced by Apter, Diprisco, Henle & Zwicker, in their joint paper:
Arthur Apter, Carlos Di Prisco, James Henle, and William Zwicker, Filter spaces: towards a unified theory of large cardinal and embedding axioms, Ann. Pure Appl. Logic 41 (1989), no. 2, 93--106.
They introduced filter space characterizations for large cardinals like measurable, supercompact and huge.
Question: Is there any filter space characterization for strong cardinals?