6 citations · 11 across the 18 of their papers we have counts for
20 papers
Zilber's notion of logically perfect structure: Universal Covers
John T. Baldwin, Andrés Villaveces
We sketch recent interactions between model theory and a roughly 150-year old study of analytic functions involving complex analysis, algebraic topology, and number theory, centere…
An almost strong relation
Shimon Garti, Andrés Villaveces
Let be a strong limit singular cardinal. We prove that if then for every ordinal . We obtain an optimal positive re…
Cartagena Logic
Siiri Kivimäki, Jouko Väänänen, Andrés Villaveces
We introduce a new kind of infinitary logic that we call Boolean expansion of . This logic involves a new kind of variable, that we call generalised Boolean vari…
Infinitary Logics and Abstract Elementary Classes
Saharon Shelah, Andrés Villaveces
We prove that every abstract elementary class (a.e.c.) with LST number and vocabulary of cardinality can be axiomatized in the logic ${\mathbb L}_{\beth_2(κ)^{+++}…
Around logical perfection
John Alexander Cruz Morales, Andrés Villaveces, Boris Zilber
In this article we present and describe a notion of "logical perfection". We extract the notion of "perfection" from the contemporary logical concept of categoricity. Categoricity…
The small index property for homogeneous models in AECs
Zaniar Ghadernezhad, Andrés Villaveces
We prove a version of a small index property theorem for strong amalgamation classes. Our result builds on an earlier theorem by Lascar and Shelah (in their case, for saturated mod…
Quantum mechanics in a metric sheaf: a model theoretic approach
Maicol A. Ochoa, Andrés Villaveces
We study model-theoretical structures for prototypical physical systems. First, a summary of the model theory of sheaves, adapted to the metric case, is presented. In particular, w…
Non-standard cohomology for equivariant sheaves: The role of generic models
Gabriel Padilla, Andres Villaveces
We generalize the Generic Model Theorem for equivariant presheaves of structures; extending the results of Macintyre and Caicedo. We also introduce a new class of generic cohomolog…
Uniqueness of Limit Models in Classes with Amalgamation
Rami Grossberg, Monica VanDieren, Andres Villaveces
We prove: Main Theorem: Let be an abstract elementary class satisfying the joint embedding and the amalgamation properties with no maximal models of cardinality .…
A global approach to AECs
Hugo Luiz Mariano, Andrés Villaveces, Pedro Hernan Zambrano
In this work we present some general categorial ideas on Abstract Elementary Classes (AECs) %\cite{She}, inspired by the totality of AECs of the form , for a fir…
Around Independence and Domination in Metric Abstract Elementary Classes, under Uniqueness of Limit Models
Andrés Villaveces, Pedro Zambrano
We study notions of independence appropriate for a stability theory of metric abstract elementary classes (for short, MAECs). We build on previous notions used in the discrete case…
Limit Models in Metric Abstract Elementary Classes: the Categorical case
Andrés Villaveces, Pedro Zambrano
We study versions of limit models adapted to the context of *metric abstract elementary classes*. Under categoricity and superstability-like assumptions, we generalize some theorem…
Sheaves of G-structures and generic G-models
Gabriel Padilla, Andrés Villaveces
In this article we give an equivariant version for the construction of generic models on presheaves of structures. We deal with first order structures endowed with a suitable actio…
Sheaves of metric structures
Maicol A. Ochoa, Andrés Villaveces
We introduce and develop the theory of metric sheaves. A metric sheaf $\A$ is defined on a topological space such that each fiber is a metric model. We describe the constructio…
Hilbert Spaces with Generic Predicates
Alexander Berenstein, Tapani Hyttinen, Andrés Villaveces
We study the model theory of expansions of Hilbert spaces by generic predicates. We first prove the existence of model companions for generic expansions of Hilbert spaces in the fo…
Uniqueness of Limit Models in Classes with Amalgamation
R. Grossberg, M. VanDieren, A. Villaveces
Let K be an abstract elementary class satisfying the joint embedding and the amalgamation properties. Let m be a cardinal above the the Löwenheim-Skolem number of the class. Suppos…
The Hart-Shelah example, in stronger logics
Saharon Shelah, Andres Villaveces
We generalize the Hart-Shelah example \cite{HaSh:323} to higher infinitary logics. We build, for each natural number and for each infinite cardinal , a sentence $ψ_k^λ…
Toward categoricity for classes with no maximal models
Saharon Shelah, Andrés Villaveces
We provide here the first steps toward Classification Theory of Abstract Elementary Classes with no maximal models, plus some mild set theoretical assumptions, when the class is ca…
Chains of End Elementary Extensions of Models of Set Theory
Andres Villaveces
Large cardinals arising from the existence of arbitrarily long end elementary extension chains over models of set theory are studied here. In particular, we show that the large car…
Heights of Models of and the Existence of End Elementary Extensions
Andres Villaveces
The existence of End Elementary Extensions of models M of ZFC is related to the ordinal height of M, according to classical results due to Keisler, Morley and Silver. In this paper…