A certain dichotomy for analytic subfamilies of P(N)

Prelegent(ci)

Jan Rossa

Afiliacja

University of Warsaw

Język referatu

polski

Termin

14 stycznia 2026 16:15

Pokój

p. 4050

Seminarium

Seminarium „Topologia i teoria mnogości”

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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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