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.

# Tag Archives: set theory

# 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 . In particular I will focus on some connections between model theoretic forcing and the model theory of abstract elementary classes.

# 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:

# 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.

# 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.

# Automorphism Groups of Homogeneous Structures. Kilpisjärvi, Finland, 1/17

A lecture on the Small Index Property and the SIP beyond First Order, given for *Arctic Set Theory 3,* and with emphasis on connections with set theory.

# Reflection Principles & Abstract Elementary Classes. Bellaterra, Catalonia, 9/16

A lecture on Reflection Principles & Abstract Elementary Classes given at the **Centre de Recerca Matemàtica** (Bellaterra, Catalunya), in the context of the *Workshop on Set-Theoretical Aspects of the Model Theory of Strong Logics*, in September of 2016.

# Categoricity in Non-Elementary contexts – The Role of Large Cardinals. Los Angeles, 4/16

For the **UCLA** Logic Seminar, in April 2016, I gave the lecture Categoricity in Non-Elementary contexts – The Role of Large Cardinals.

# Model Theory of Abstract Elementary Classes: some recent trends. Tehran, 11/15

Here are (very sketchy) notes for a minicourse called Model Theory of Abstract Elementary Classes: some recent trends. I gave that minicourse at the IPM in November 2015. The four two-hour sessions were:

**Day 1:**The early days of AECs**Day 2:**Stability Theory of AECs**Day 3:**Stability Theory of AECs (II)**Day 4:**Connections with Set Theory**Appendix:**more examples

# Categoricità, dalla teoria dei modelli alla teoria degli insiemi? Torino, 6/15

For the Logic Seminar at the University of Turin in June 2015 I gave the lecture Categoricità, dalla teoria dei modelli alla teoria degli insiemi? (Categoricity, from Model Theory to Set Theory?)