Para el Coloquio del Departamento de Matemáticas de la Universidad Nacional de Colombia, dí la conferencia Matemáticas condensadas y forcing: una primera lectura.
He aquí las notas de conferencia:
Tag Archives: set theory
Grandes cardinales virtuales y genéricos (y algo de teoría de modelos). Bogotá, 4/25
Para el Seminario de Teoría de Conjuntos de la Universidad de los Andes (Bogotá), di en abril de 2025 la conferencia Grandes cardinales virtuales y genéricos (y algo de teoría de modelos).
Some recent (and some not so recent) interactions between Set Theory and Model Theory – Kobe, 3/25
For the Kobe Logic Seminar (and for the Kobe Set Theory Seminar) at Kobe University (Kobe, Japan), I gave the lecture Some recent (and some not so recent) interactions between Set Theory and Model Theory in March 2025.
Dos lógicas extrañas, grandes cardinales y algo de forcing. Morelia, 12/22
For the Seminario de Topología y Teoría de Conjuntos at UNAM in Morelia, I gave a lecture where a blend of infinitary logic, large cardinals and forcing were explored.
Tra teoria dei modelli e teoria degli insiemi – Torino (v) – 5/21
As part of my Torino Lectures in Set Theory, Special Lecture 3 was given in Italian. The title was Tra teoria dei modelli e teoria degli insiemi.
La terza lezione speciale (parte del corso Teoria degli insieme) sarà questo prossimo giovedì (16:30 ore a Torino). Darò io stesso la lezione stavolta, su connessioni tra teoria dei modelli e teoria degli insiemi. La lezione sarà diretta principalmente a studenti che iniziano il loro apprendimento delle tecniche di forcing e grandi cardinali (la lezione 2, che Vika Gitman ha dato due settimane fa, anche aveva un mix di questi due temi).
Sarà anche la prima volta che parlerò in italiano in pubblico online (forse soltanto per una parte della lezione; dipende di come andrà tutto). Ho invitato gente che in principio può capire la lezione così.
Two logics, and their connections with large cardinals / Questions for BDGM – New York (v) – 4/21
For the CUNY Graduate Center Set Theory Seminar I gave a series of two lectures with title Two logics, and their connections with large cardinals / Questions for BDGM.
Abstract: In the past couple of years I have been involved (joint work with Väänänen and independently with Shelah) with some logics in the vicinity of Shelah’s 
These logics seem to have additional interesting properties under the further assumption of strong compactness of a cardinal, and this brings them close to recent work of Boney, Dimopoulos, Gitman and Magidor [BDGM].
During the first lecture, I plan to describe two games and a syntax of two logics: Shelah’s 
During the second lecture, I plan to enter rather uncharted territory. I will describe some constructions done by Shelah (mostly) under the assumption of strong compactness, but I also plan to bring these logics to a territory closer to the work of [BDGM]. This second lecture will have more conjectures, ideas, and (hopefully interesting) discussions with some of the authors of that paper.
Tree Partition Properties / natural logics for AEC (a tale of two cities) – Bogotá 11/19
During DiPriscoFest I gave the lecture Tree Partition Properties / natural logics for AEC (a tale of two cities) as homage to Carlos Di Prisco, the Caracas Logic Group and the Intertwined History of two Logic Groups: Caracas and Bogotá.
Interpolation and model theoretic forcing – some new perspectives (Campinas, Brazil, 12/18)
Interpolation and model theoretic forcing – some new perspectives.
(A lecture in Cantor Meets Robinson – Set theory, model theory and their philosophy. University of Campinas, Brazil, December 2018.)
Model Theoretic Forcing has been interweaved with interpolation theorems in infinitary logic since the early work of Mostowski, Vaught, Harnik and others. I will present some of these historical connections and their effect on Shelah’s much more recent logic
Infinitary logic, large cardinals and AECs: some reflections (Montseny, Catalunya, 11/18)
Reflections on Set Theoretic Reflection – Montseny, Catalunya, nov. 2018.
Infinitary logic, large cardinals and AECs: some reflections.
Abstract:
The interaction between infinitary logic and the model theory of abstract elementary classes has had a serious imprint of large cardinals since the inception of AECs. Although later developments in AECs have emphasized a more purely model theoretic treatment, capturing independence-like relations, there are various fundamental questions on the relation between various logics and AECs — and, in some of these, large cardinals are central.
I will discuss some work by Boney on these connections, as well as some recent joint work by Väänänen and myself.
Entre ZFC y HoTT – sobre posibles crisis … (Medellín, 10/18)
Coloquio – Escuela de Matemáticas – Universidad Nacional de Colombia – Medellín
1 de octubre de 2018
Entre ZFC y HoTT – sobre posibles crisis de fundamentos en la matemática
Resumen: Se ha hablado recientemente de una nueva crisis en los fundamentos de la matemática, en relación con la propuesta originada en trabajos de Voevodsky sobre la “teoría homotópica de tipos” (Homotopy Type Theory, mejor conocida por su acrónimo HoTT) y una posible re-fundamentación de la matemática basada en esta. Hace poco más de un siglo hubo otra crisis que finalmente se decantó en la axiomatización de Zermelo y Fraenkel. Daré un panorama de lo qué está pasando realmente en HoTT y con el nuevo Axioma UF (Univalent Foundations), y trataré de poner en perspectiva la pregunta sobre la crisis. Esta charla se ubicará entre los dos extremos conjuntista y “tipo-teórico-homotópico”: el debate sobre el tema ha tenido contribuciones interesantes de Dzamonja (del lado conjuntístico) y Lurie (crítico, desde el lado categórico). Mostraré algo del debate reciente.
Andrés Villaveces 