Sobre la superestabilidad en Q-Clases elementales abstractas

Vista sencilla de ítem
dc.contributor.advisorZambrano Ramirez, Pedro Hernánspa
dc.contributor.authorNájar Salinas, José Nicolásspa
dc.contributor.researchgroupInteracciones entre teoría de modelos, categorías, conjuntos y geometría algebraicaspa
dc.date.accessioned2020-08-06T00:43:59Zspa
dc.date.available2020-08-06T00:43:59Zspa
dc.date.issued2020-08-04spa
dc.description.abstractIn the present work we study the concept of Q-abstract elementary class and we do an approximation to superestability in this context, adapting Shelah-Villaveces theorem. With the help of this theorem and based on chapter 15 of [Bal09], we studied the saturation of the union of chains of saturated as a weak notion of superstability.spa
dc.description.abstractEn el presente trabajo estudiamos el concepto de Q-clase elemental abstracta y hacemos una aproximación a la superestabilidad en este contexto adaptando el teorema de Shelah-Villaveces (teorema 2.1 en [SV99]). Con ayuda de este teorema y basándonos en lo expuesto por Baldwin en el capítulo 15 de [Bal09], estudiamos la saturación de la unión de cadenas de modelos saturados como una noción débil de superestabilidad.spa
dc.description.additionalLínea de Investigación: Teoría de Modelos.spa
dc.description.commentsnicolas.na7ar@gmail.comspa
dc.description.degreelevelMaestríaspa
dc.format.extent223spa
dc.format.mimetypeapplication/pdfspa
dc.identifier.urihttps://repositorio.unal.edu.co/handle/unal/77951
dc.language.isospaspa
dc.publisher.branchUniversidad Nacional de Colombia - Sede Bogotáspa
dc.publisher.departmentDepartamento de Matemáticasspa
dc.publisher.programBogotá - Ciencias - Maestría en Ciencias - Matemáticasspa
dc.relation.referencesUri Abraham and Menachem Magidor. Cardinal arithmetic. In Handbook of set theory, pages 1149–1227. Springer, 2010.spa
dc.relation.referencesJohn T Baldwin. Ehrenfeucht-mostowski models in abstract elementary classes. Contemporary Mathematics, 380:1–16, 2005.spa
dc.relation.referencesJohn T Baldwin. Categoricity, volume 50. American Mathematical Soc., 2009.spa
dc.relation.referencesWill Boney and Rami Grossberg. Forking in short and tame abstract elementary classes. Annals of Pure and Applied Logic, 168(8):1517–1551, 2017.spa
dc.relation.referencesWill Boney, Rami Grossberg, Monica M VanDieren, and Sebastien Vasey. Superstability from categoricity in abstract elementary classes. Annals of Pure and Applied Logic, 168(7):1383–1395, 2017.spa
dc.relation.referencesJohn Baldwin, David Kueker, Monica VanDieren, et al. Upward stability transfer for tame abstract elementary classes. Notre Dame Journal of Formal Logic, 47(2):291–298, 2006.spa
dc.relation.referencesWill Boney. Tameness from large cardinal axioms. The Journal of Symbolic Logic, 79(4):1092–1119, 2014.spa
dc.relation.referencesTibor Beke and Jirí Rosickỳ. Abstract elementary classes and accessible categories. Annals of Pure and Applied Logic, 163(12):2008–2017, 2012.spa
dc.relation.referencesWill Boney and Sebastien Vasey. A survey on tame abstract elementary classes. arXiv preprint arXiv:1512.00060, 2015.spa
dc.relation.referencesWill Boney, Monica M VanDieren, and Sebastien Vasey. Shelah-villaveces revisited. arXiv preprint arXiv:1611.05292, 2016.spa
dc.relation.referencesAndrew H Coppola. The theory of Q-Abstract Elementary Classes. PhD thesis, University of Illinois at Chicago, 2006.spa
dc.relation.referencesAndrzej Ehrenfeucht and Andrzej Mostowski. Models of axiomatic theories admitting automorphisms. Fund. Math, 43:50–68, 1956.spa
dc.relation.referencesChristian Espíndola. A topos-theoretic proof of shelah’s eventual categoricity conjecture for abstract elementary classes. arXiv preprint arXiv:1906.09169, 2019.spa
dc.relation.referencesRami Grossberg and Monica VanDieren. Galois-stability for tame abstract elementary classes. Journal of Mathematical Logic, 6(01):25–48, 2006.spa
dc.relation.referencesRami Grossberg and Monica VanDieren. Shelah’s categoricity conjecture from a successor for tame abstract elementary classes. Journal of Symbolic Logic, pages 553–568, 2006.spa
dc.relation.referencesRami Grossberg and Sebastien Vasey. Equivalent definitions of superstability in tame abstract elementary classes. The Journal of Symbolic Logic, 82(4):1387–1408, 2017.spa
dc.relation.referencesRami Grossberg, Monica VanDieren, and Andrés Villaveces. Uniqueness of limit models in classes with amalgamation. Mathematical Logic Quarterly, 62(4-5):367–382, 2016.spa
dc.relation.referencesThomas Jech. Set theory. the third millennium edition. Springer Monographs in Mathematics. Springer-Verlag, 2003.spa
dc.relation.referencesOlivier Lessmann. An introduction to uncountable categoricity in abstract elementary classes, volume 6 of graduate texts in mathematics. University of Helsinki, Department of Mathematics and Statistics, 2005.spa
dc.relation.referencesMichael J Lieberman. Category-theoretic aspects of abstract elementary classes. Annals of Pure and Applied Logic, 162(11):903–915, 2011.spa
dc.relation.referencesMichael Lieberman and Jiri Rosicky. Approximations of superstability in concrete accessible categories. arXiv preprint arXiv:1505.06047, 2015.spa
dc.relation.referencesMichael Lieberman and Jirí Rosickỳ. Classification theory for accessible categories. The Journal of Symbolic Logic, 81(1):151–165, 2016.spa
dc.relation.referencesMichael Lieberman and Jirí Rosickỳ. Metric abstract elementary classes as accessible categories. The Journal of Symbolic Logic, 82(3):1022–1040, 2017.spa
dc.relation.referencesMichael Lieberman, Jiří Rosickỳ, and Sebastien Vasey. Forking independence from the categorical point of view. arXiv preprint arXiv:1801.09001, 2018.spa
dc.relation.referencesDavid Marker. Model theory: an introduction, volume 217. Springer Science & Business Media, 2006.spa
dc.relation.referencesMichael Makkai and Robert Paré. Accessible categories: the foundations of categorical model theory, volume 104. American Mathematical Soc., 1989.spa
dc.relation.referencesMichael Makkai and Saharon Shelah. Categoricity of theories in l κω , with κ a compact cardinal. Annals of Pure and Applied Logic, 47(1):41–97, 1990.spa
dc.relation.referencesAnand Pillay. An introduction to stability theory. Courier Corporation, 2008.spa
dc.relation.referencesSaharon Shelah. Categoricity in א 1 of sentences in L , ω 1 ,ω (q). Israel Journal of Mathematics, 20(2):127–148, 1975.spa
dc.relation.referencesSaharon Shelah. Classification of non elementary classes ii abstract elementary classes. In Classification theory, pages 419–497. Springer, 1987.spa
dc.relation.referencesSaharon Shelah. Universal classes. In Classification theory, pages 264–418. Springer, 1987. Saharon Shelah. Cardinal arithmetic, volume 3. Oxford, 1994.spa
dc.relation.referencesSaharon Shelah. Categoricity for abstract classes with amalgamation. Annals of Pure and Applied Logic, 98(1-3):261–294, 1999.spa
dc.relation.referencesSaharon Shelah and Andrés Villaveces. Toward categoricity for classes with no maximal models. Annals of Pure and Applied Logic, 97(1-3):1–25, 1999.spa
dc.relation.referencesSaharon Shelah and Sebastien Vasey. Categoricity and multidemensional diagrams. 2018. Katrin Tent and Martin Ziegler. A course in model theory, volume 40. Cambridge University Press, 2012.spa
dc.relation.referencesMonica VanDieren. Categoricity in abstract elementary classes with no maximal models. Annals of Pure and Applied Logic, 141(1-2):108–147, 2006.spa
dc.relation.referencesMonica M VanDieren. Symmetry and the union of saturated models in superstable abstract elementary classes. Annals of Pure and Applied Logic, 167(4):395–407, 2016.spa
dc.relation.referencesSebastien Vasey. Downward categoricity from a successor inside a good frame. Annals of Pure and Applied Logic, 168(3):651–692, 2017.spa
dc.relation.referencesSebastien Vasey. Saturation and solvability in abstract elementary classes with amalgamation. Archive for Mathematical Logic, 56(5-6):671–690, 2017.spa
dc.relation.referencesSebastien Vasey. Superstability and Categoricity in Abstract Elementary Classes. PhD thesis, Carnegie Mellon Unievrsity, 2017.spa
dc.relation.referencesPedro Zambrano. Around superstability in metric abstract elementary classes. PhD thesis, Universidad Nacional de Colombia sede Bogotá, 2011.spa
dc.rights.accessrightsinfo:eu-repo/semantics/openAccessspa
dc.rights.licenseCC0 1.0 Universalspa
dc.rights.spaAcceso abiertospa
dc.rights.urihttp://creativecommons.org/publicdomain/zero/1.0/spa
dc.subject.ddc510 - Matemáticasspa
dc.subject.ddc516 - Geometríaspa
dc.subject.ddc512 - Álgebraspa
dc.subject.proposalQ-abstract elementary classeng
dc.subject.proposalQ-Clase Elemental Abstractaspa
dc.subject.proposalsuperestabilidadspa
dc.subject.proposalsuperstabilityeng
dc.subject.proposalteorema de Shelah-Villavecesspa
dc.subject.proposalsaturationeng
dc.subject.proposalshelah-Villaveces theoremeng
dc.subject.proposalsaturaciónspa
dc.titleSobre la superestabilidad en Q-Clases elementales abstractasspa
dc.typeDocumento de trabajospa
dc.type.driverinfo:eu-repo/semantics/workingPaperspa
dc.type.versioninfo:eu-repo/semantics/acceptedVersionspa
oaire.accessrightshttp://purl.org/coar/access_right/c_abf2spa

Archivos

Bloque original

Mostrando 1 - 1 de 1
Miniatura
Nombre:
Sobre la Superestabilidad en Q-Clases Elementales Abstractas.pdf
Tamaño:
1.41 MB
Formato:
Adobe Portable Document Format
Descargar

Bloque de licencias

Mostrando 1 - 1 de 1
Miniatura
Nombre:
license.txt
Tamaño:
3.8 KB
Formato:
Item-specific license agreed upon to submission
Descripción:
Descargar

Colecciones

Maestría en Ciencias - Matemáticas