A certain dichotomy for analytic subfamilies of P(N)

Speaker(s)

Jan Rossa

Affiliation

University of Warsaw

Language of the talk

Polish

Date

Jan. 14, 2026, 4:15 p.m.

Room

room 4050

Seminar

Topology and Set Theory Seminar

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In this talk we will discuss a complete proof of a certain dichotomy for analytic subfamilies of P(N) (endowed with the Cantor set topology via characteristic functions), originally stated in G. Godefroy's work "Compacts de Rosenthal", Pac. J. Math. 91, 293-306 (1980). 
The dichotomy can be equivalently reformulated as the statement that for any analytic splitting family F, there exists an infinite subset S of natural numbers such that, by intersecting elements of F with S, we obtain exactly P(S). The presented proof of the dichotomy is mainly an adaptation of the proof of one of the well-known Rosenthal's dichotomies.

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