**Continuity of coordinate functionals **for filter Schauder basis without Large Cardinals

During my talk in November, I presented joint results with Tomasz Kania about using the large cardinals to positively answer the Kadets problem about coontinuity of coordinate functionals related to filter Schauder basis. This time I will present results obtained jointly with Tomasz Kania and Noe de Rancourt, which gives a positive answer to Kadets’ question in ZFC for analytic filters. I will also show that each filter basis with continuous coordinate functionals is also a basis with respect to some analytic filter.

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