Andrés Villaveces - research
Research papers:
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Extensions of Models
of Set Theory: Height and Large Cardinals, (Ph. D. thesis -
University of Wisconsin-Madison, adviser: Kenneth Kunen, 1996),
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Heights of Models of ZFC and the Existence of End Elementary
Extensions,
in the volume `Models, Algebras and Proofs', eds. X. Caicedo &
C. Montenegro,
Lecture Notes in Pure and Applied Mathematics, vol. 203, Marcel Dekker,
New York, 1999.
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Heights of Models
of ZFC and the Existence of End Elementary Extensions II, The Journal of Symbolic Logic, volume 64, number 3, September 1999, pages 1111-1124,
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Chains of
End Elementary Extensions of Models of Set Theory, The Journal
of Symbolic Logic, volume 63, number 3, September 1998, pages 1116-1136,
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Toward
categoricity for classes with no maximal models, with Saharon Shelah,
Annals of Pure and Applied Logic, volume 97, 1999, pp. 1-25.[abstract],
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On ec structures in abstract elementary classes, with Javier Moreno. In
preparation.
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The
Failure of GCH at Unfoldable Cardinals, with Amir Leshem, accepted
by JSL, under revisions.
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Shooting a club through an unfoldable cardinal, with Franqui
Cárdenas. In preparation.
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Categoricity may fail late, with Saharon
Shelah. Submitted in 2002.
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Uniqueness of Limit Models in Classes
with Amalgamation, with
Rami Grossberg and
Monica VanDieren.
Submitted.
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Hrushovski fusions and Tame Abstract Elementary Classes, with
Pedro Zambrano. In preparation.
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Hilbert Spaces with Generic Predicates, with Alexander
Berenstein. Submitted in 2007.
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Abelian Groups as Abstract Elementary Classes, ongoing work
with John Baldwin, Wesley Calvert, John Goodrick and Agatha Walczak-Typke.
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Laver Diamonds on Strongly Unfoldable Cardinals, with Franqui Cárdenas.
In preparation.
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Stability Spectrum and Predicates in Continuous Model Theory, with Alexander Berenstein. In preparation.
Some survey papers
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De
Los al presente: un teorema aún central en teoría
de la clasificación. Boletín de Matemáticas,
Nueva Serie, volumen IV, número 1, Junio de 1997 (written in 1998,
appeared in early 1999). This is a survey on the extension of Classification
Theory to Abstract Elementary Classes.
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Alephω
de aleph a omega. Boletín de Matemáticas, Nueva Serie,
volumen IV, número 1, Junio de 1997 (written in 1998, appeared in
early 1999).
- La tensión entre
Teoría de Modelos y Análisis Matemático:
Estabilidad y la exponencial compleja. Submitted in 2004. Last
Update: Jan 20 2005
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Set theoretical issues in Abstract Elementary Classes. In preparation.
Slides of some talks
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Categoricity
theorems may fail for abstract elementary classes,
contributed talk at the European
Logic Colloquium, Paris, 2000.
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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).
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Categoricity theorems may fail for abstract elementary classes,
invited talk at the MAMLS Meeting, Rutgers, February 2001.
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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.
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On abstract elementary classes,
invited talk at the logic seminar,
University of Illinois at Chicago, November 2001.
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Classifying mathematical structures; some trends in model theory,
colloquium talk at Carnegie-Mellon University, Pittsburgh, April 2002.
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On excellent classes,
MAMLS Meeting at Carnegie-Mellon University, Pittsburgh, November 2002.
Lecture notes (in Spanish)
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Categoricidad, de Morley a nuestros
días. In Spanish, a graduate course on aspects of
categoricity from Morley's proof to [Sh 394].
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Lógica III (filosofía)- (In Spanish) Historia
de la Lógica Matemática entre 1870 y 1930 (Cantor - Peirce
- Hilbert - Russell - Skolem - Gödel). Teorías del Infinito.
ZF. Historia de los inicios de la teoría de modelos. Teoremas de
Gödel, Löwenheim-Skolem, paradojas de Cantor, Russell y Skolem.
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Teoría Avanzada de Conjuntos. In spanish, notes of the Set
Theory class, from scratch to (non iterated) forcing.
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