mathematics research

Selected publications

Research paOLYMPUS DIGITAL CAMERApers:

    • The Small Index Property for Homogeneous Models in AEC’s. To appear in Archive for Mathematical Logic; a volume devoted to the proceedings of the IPM Conference on Set Theory and Model Theory, October 2015 (with Zaniar Ghadernezhad).
  • Uniqueness of Limit Models in Classes with Amalgamation. Math. Log. Quart. 62, No. 4–5, 367–382 (2016) (with Rami Grossberg and Monica VanDieren).
  • Sheaves of metric structures. Logic, Language, Information, and Computation (23rd International Workshop, WoLLIC 2016, Puebla, Mexico, August 16-19th, 2016. Proceedings, with Maicol Ochoa).
  • Around Stability Theory of Sheaves. 2014.
  • A global approach to AECs. (2014, with Hugo Luiz Mariano and Pedro Zambrano).
  • Around independence and domination in metric abstract elementary classes: assuming uniqueness of limit models. Math. Log. Quart. 60, No. 3, 211–227 (2014)  (with Pedro Zambrano).
  • Limit Models in Metric Abstract Elementary Classes: the Categorical case. (2013, with Pedro Zambrano).
  • The Two-Cardinal Problem, with Omitting Types (2013, with Luis Miguel Villegas).
  • Sheaves of G-structures and generic G-models. (2012, with Gabriel Padilla).
  • Hilbert Spaces with Generic Predicates. Accepted by Archiv for Mathematical Logic, undergoing modifications. (2011, with Alexander Berenstein).
  • Hrushovski fusions and Tame Abstract Elementary Classes. (2006, with Pedro Zambrano).
  • Notions of Independence for Metric Abstract Elementary Classes. The Royal Swedish Academy of Sciences – Mittag-Leffler Institute. Preprint series. Fall 2009. (With Pedro Zambrano)
  • Around Superstability in Metric Abstract Elementary Classes: Limit Models and r-Towers. The Royal Swedish Academy of Sciences – Mittag-Leffler Institute. Preprint series. Fall 2009. (With Pedro Zambrano).
  • Categoricity may fail late. Submitted to Journal of Symbolic Logic. 2008. (With Saharon Shelah).
  • Laver Diamonds on Strongly Unfoldable Cardinals. (2003, with Franqui Cárdenas).
  • Beautiful pairs in continuous model theory. (In preparation, with Alexander Berenstein).
  • On categoricity spectra for classes with no maximal models II. (In preparation, with Saharon Shelah).
  • Toward categoricity for classes with no maximal models. Annals of Pure and Applied Logic 97, 1999, 1–25 (with Saharon Shelah).
  • Heights of Models of ZFC and the Existence of End Elementary Extensions II. The Journal of Symbolic Logic 64-3, Sept. 1999.
  • Chains of End Elementary Extensions of Models of Set Theory. The Journal of Symbolic Logic 63-3, Sept. 1998.

Scientific Books (Monographs):

  • (Editor, with Roman Kossak, Juha Kontinen and Åsa Hirvonen): Logic Without Borders. A volume in honor of Jouko Väänänen’s Sixtieth Birthday. To appear (De Gruyter).
  • La tricotomía de Zilber: una breve introducción geométrica. (Zilber’s Trichotomy: a brief geometric introduction) Book in the series Publicaciones de la XXIV Escuela Venezolana de Matemáticas y EMALCA – Ediciones IVIC – Venezuela 2011. 95 pages.

Reviews:

Surveys:

  • \aleph_\omega de aleph a omega. Boletín de Matemáticas. IV – 1. June 1997.
  • La Conjetura de Łoś: un teorema aún central en Teoría de la Clasificación. Boletín de Matemáticas. IV – 1. June 1997.
  • Heights of Models of ZFC and the Existence of End Elementary Extensions, in Models, Algebras and Proofs, eds: Xavier Caicedo and Carlos Montenegro (Tenth Latin American Symposium in Mathematical Logic, Bogotá, 1995), 1999.

 

Lectures (with some slides).

  • II Encontro de Topologia e Teoria dos Conjuntos, Salvador de Bahia, February 2012.
  • Lecture “Some Set-Theoretic Dichotomies in Model Theory”, Kobe, Japan, January 2012.
  • Lecture for Logic Seminar “Dicotomies en théorie des modèles”, Lyon, Francia, November 2011.
  • Infinity Conference – Centre de Recerca Matemàtica – Bellaterra, Catalonia, July 2011.
  • Stability Theory of Polish Spaces, Helsinki, June 2011.
  • Philosophy Symposium on the Logic of Sheaves, within the Colombian Congress of Philosophy – Cali, Colombia, October 2010.
  • The Model Theory of Sheaves (minicourse) – Jouko Väänänen’s Sixtieth Birthday Conference. Helsinki, September 2010.
  • Barcelona Logic Seminar. September 2010: On type decomposition in NIP theories.
  • Infinity Conference – Centre de Recerca Matemàtica – Bellaterra, Catalonia, 2010: Around forcing categoricity of a bipartite random graph, at \aleph_2.
  • Mittag-Leffler Institute – Octubre de 2009: \kappa-dependent AECs.
  • European Science Foundation – Model Theory – Mathematical Research and Conference Center – Będlewo – Polonia. July 2009.
  • Kunen Fest: Topology and Set Theory Conference, april 2009, Madison, Wisconsin: Metric Continuous Abstract Elementary Classes Why? Superstability, NIP, examples.
  • Logic Seminar, Universidad Autónoma Metropolitana – Mexico City – October 2008 – Clases Elementales Abstractas e invariantes geométricos.
  • Logic Seminar, University of East Anglia, Norwich, Inglaterra, July 2008. Continuous Model Theory – Some simplicity issues.
  • XIV SLALM – Paraty, Brasil: Continuous Model Theory, Metric AECs: Simplicity issues, expansions by predicates. May 2008.
  • Logic Seminar, Università di Torino: Abstract Elementary Classes: A middle ground of generalization. December 2007.
  • Logic Seminar, Universidad de Barcelona, november 2007: Expansions amb predicats en lògica continua: Estabilitat i simplicitat.
  • Aesthetics and Mathematics Symposium, Universidad de Utrecht (The Netherlands), november 2007: Higher Amalgams: the wonderful mélange.
  • Southern Wisconsin Logic Colloquium, Madison, Wisconsin, october 2007: Generic Predicates in Continuous Model Theory.
  • Lecture for the American Mathematical Society Sectional Meeting, Chicago, October 2007: Around simplicity in various non-elementary classes.
  • Colombian Congress of Mathematics, 2007: Teoría de Modelos de Espacios de Hilbert: pares buenos y menos buenos. Cleas versus gatos.
  • Logic Seminar, Université Claude-Bernard Lyon-I (France), june 2007: Espaces de Hilbert et Prédicats Génériques: deux exemples et quelques questions.
  • Helsinki Logic Seminar, june 2007: On Simplicity in Continuous Model Theory.
  • (towards a) Model Theory for Chemical Reaction. Logic Seminar. University of Helsinki, April 2007.
  • Generic Predicates over Hilbert Spaces – (Continuous) Model Theory of Pairs. Colloquium on Mathematical Logic, Universiteit van Amsterdam. March 2007.
  • Abstract Elementary Classes and Finite Combinatorics. Finite Model Theory Seminar, University of Tampere, Finland, February 2007.
  • Generic Predicates in Continuous Model Theory. Logic Seminar. University of Helsinki, February 2007.
  • Classifying mathematical structures; some trends in model theory, colloquium talk at Carnegie-Mellon University, Pittsburgh, April 2002.
  • On abstract elementary classes, invited talk at the logic seminar, University of Illinois at Chicago, November 2001.
  • The weak expressive power of First Order Logic in Mathematics, and the strength of this limitation, invited talk at the joint mathematics and philosophy symposium, Carnegie-Mellon University, Pittsburgh, October 2001.
  • Categoricity theorems may fail for abstract elementary classes, invited talk at the MAMLS Meeting, Rutgers, February 2001.
  • Lógica en Álgebra y Análisis: caminos para sacarle jugo a las limitaciones expresivas, invited colloquium talk at Universidad de los Andes, October 2000 (in Spanish).
  • Categoricity theorems may fail for abstract elementary classes, contributed talk at the European Logic Colloquium, Paris, 2000.