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This talk explores the construction of a separable Banach space with Baire order 2, addressing an open question posed by Argyros, Godefroy, and Rosenthal. Learn about intrinsic Baire classes of separable Banach spaces, which are defined recursively as iterated weak* sequential closures of the canonical image of X in X**. Discover how the speaker and collaborators Anna Pelczar-Barwacz and Tomasz Wawrzycki solved this problem by constructing a space with Baire order 2, providing the first example between the previously known orders of 0, 1, and omega_1. This 17-minute presentation was delivered as part of the Workshop on "Structures in Banach Spaces" held at the Erwin Schrödinger International Institute for Mathematics and Physics in March 2025.
