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This 17-minute conference talk from the Workshop on "Structures in Banach Spaces" at the Erwin Schrödinger International Institute for Mathematics and Physics (ESI) explores the concept of L-orthogonality and its connections to set theory. Discover how L-orthogonality, which has been extensively researched due to its relationship with copies of l_1, intersects with set theory through special ultrafilters, particularly Q-points. Learn about Q-measures as a generalization of Q-points, their connection to L-orthogonality research, and various consistency and independence results. The presentation represents joint work by Luis David Reyes Sáenz with Antonio Avilés, Gonzalo Martínez Cervantes, and Alejando Poveda, delivered during the March 17-21, 2025 workshop at ESI.
