Author Archives: a v n

Logics underlying Abstract Elementary Classes (Warsaw, 4/18)

 
Abstract: I will first describe Abstract Elementary Classes as a global generalization of Infinitary Logic. I will emphasize constructions such as Galois types, the Representation Theorem and various open problems. In the second half, I will focus on some recent research on logics underlying AECs – with special emphasis on Shelah’s L^1_\kappa logic (satisfying Interpolation and weak remnants of compactness) and the role it plays in controlling Abstract Elementary Classes. This second part contains recent results of research and several open questions.
Logic Seminar, University of Warsaw.

Some interactions / model theory and set theory (Mexico City, 1/18)

(slides)

Some connections first between categoricity in model theory and the role of large cardinals in pinning down tameness (work of Boney and Unger), with a slight reframing of Boney’s proof. Then, more model theory and set theory connections, around the combinatorics of pcf structures, problems of absoluteness and tree properties.

1st Mexico-USA Logicfest – ITAM, Mexico City, January 2018.

Mentes experimentales de Papy y Jeangros: ¿surrealismo? ¿fenomenología? ?!? Bogotá, 3/17

A lecture for Seminario Papy de Matemáticas Elementales – Universidad Nacional, Bogotá – March 2017.

An attempt to link the enormous pedagogical work of Belgian mathematician Georges Papy in the world, and his influence in Colombia through the work of Swiss pedagogue Roland Jeangros with other intellectual movements of their time.