Sobre la superestabilidad en Q-Clases elementales abstractas
In 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 a...
- Autores:
-
Nájar Salinas, José Nicolás
- Tipo de recurso:
- Fecha de publicación:
- 2020
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/77951
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/77951
- Palabra clave:
- 510 - Matemáticas
516 - Geometría
512 - Álgebra
Q-abstract elementary class
superstability
saturation
shelah-Villaveces theorem
Q-Clase Elemental Abstracta
superestabilidad
teorema de Shelah-Villaveces
saturación
- Rights
- License
- CC0 1.0 Universal
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Sobre la superestabilidad en Q-Clases elementales abstractas |
| title |
Sobre la superestabilidad en Q-Clases elementales abstractas |
| spellingShingle |
Sobre la superestabilidad en Q-Clases elementales abstractas 510 - Matemáticas 516 - Geometría 512 - Álgebra Q-abstract elementary class superstability saturation shelah-Villaveces theorem Q-Clase Elemental Abstracta superestabilidad teorema de Shelah-Villaveces saturación |
| title_short |
Sobre la superestabilidad en Q-Clases elementales abstractas |
| title_full |
Sobre la superestabilidad en Q-Clases elementales abstractas |
| title_fullStr |
Sobre la superestabilidad en Q-Clases elementales abstractas |
| title_full_unstemmed |
Sobre la superestabilidad en Q-Clases elementales abstractas |
| title_sort |
Sobre la superestabilidad en Q-Clases elementales abstractas |
| dc.creator.fl_str_mv |
Nájar Salinas, José Nicolás |
| dc.contributor.advisor.spa.fl_str_mv |
Zambrano Ramirez, Pedro Hernán |
| dc.contributor.author.spa.fl_str_mv |
Nájar Salinas, José Nicolás |
| dc.contributor.researchgroup.spa.fl_str_mv |
Interacciones entre teoría de modelos, categorías, conjuntos y geometría algebraica |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas 516 - Geometría 512 - Álgebra |
| topic |
510 - Matemáticas 516 - Geometría 512 - Álgebra Q-abstract elementary class superstability saturation shelah-Villaveces theorem Q-Clase Elemental Abstracta superestabilidad teorema de Shelah-Villaveces saturación |
| dc.subject.proposal.eng.fl_str_mv |
Q-abstract elementary class superstability saturation shelah-Villaveces theorem |
| dc.subject.proposal.spa.fl_str_mv |
Q-Clase Elemental Abstracta superestabilidad teorema de Shelah-Villaveces saturación |
| description |
In 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. |
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2020 |
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2020-08-06T00:43:59Z |
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2020-08-06T00:43:59Z |
| dc.date.issued.spa.fl_str_mv |
2020-08-04 |
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Documento de trabajo |
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http://purl.org/coar/resource_type/c_8042 |
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info:eu-repo/semantics/workingPaper |
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https://repositorio.unal.edu.co/handle/unal/77951 |
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https://repositorio.unal.edu.co/handle/unal/77951 |
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spa |
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spa |
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Uri Abraham and Menachem Magidor. Cardinal arithmetic. In Handbook of set theory, pages 1149–1227. Springer, 2010. John T Baldwin. Ehrenfeucht-mostowski models in abstract elementary classes. Contemporary Mathematics, 380:1–16, 2005. John T Baldwin. Categoricity, volume 50. American Mathematical Soc., 2009. Will Boney and Rami Grossberg. Forking in short and tame abstract elementary classes. Annals of Pure and Applied Logic, 168(8):1517–1551, 2017. Will 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. John 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. Will Boney. Tameness from large cardinal axioms. The Journal of Symbolic Logic, 79(4):1092–1119, 2014. Tibor Beke and Jirí Rosickỳ. Abstract elementary classes and accessible categories. Annals of Pure and Applied Logic, 163(12):2008–2017, 2012. Will Boney and Sebastien Vasey. A survey on tame abstract elementary classes. arXiv preprint arXiv:1512.00060, 2015. Will Boney, Monica M VanDieren, and Sebastien Vasey. Shelah-villaveces revisited. arXiv preprint arXiv:1611.05292, 2016. Andrew H Coppola. The theory of Q-Abstract Elementary Classes. PhD thesis, University of Illinois at Chicago, 2006. Andrzej Ehrenfeucht and Andrzej Mostowski. Models of axiomatic theories admitting automorphisms. Fund. Math, 43:50–68, 1956. Christian Espíndola. A topos-theoretic proof of shelah’s eventual categoricity conjecture for abstract elementary classes. arXiv preprint arXiv:1906.09169, 2019. Rami Grossberg and Monica VanDieren. Galois-stability for tame abstract elementary classes. Journal of Mathematical Logic, 6(01):25–48, 2006. Rami Grossberg and Monica VanDieren. Shelah’s categoricity conjecture from a successor for tame abstract elementary classes. Journal of Symbolic Logic, pages 553–568, 2006. Rami Grossberg and Sebastien Vasey. Equivalent definitions of superstability in tame abstract elementary classes. The Journal of Symbolic Logic, 82(4):1387–1408, 2017. Rami Grossberg, Monica VanDieren, and Andrés Villaveces. Uniqueness of limit models in classes with amalgamation. Mathematical Logic Quarterly, 62(4-5):367–382, 2016. Thomas Jech. Set theory. the third millennium edition. Springer Monographs in Mathematics. Springer-Verlag, 2003. Olivier 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. Michael J Lieberman. Category-theoretic aspects of abstract elementary classes. Annals of Pure and Applied Logic, 162(11):903–915, 2011. Michael Lieberman and Jiri Rosicky. Approximations of superstability in concrete accessible categories. arXiv preprint arXiv:1505.06047, 2015. Michael Lieberman and Jirí Rosickỳ. Classification theory for accessible categories. The Journal of Symbolic Logic, 81(1):151–165, 2016. Michael Lieberman and Jirí Rosickỳ. Metric abstract elementary classes as accessible categories. The Journal of Symbolic Logic, 82(3):1022–1040, 2017. Michael Lieberman, Jiří Rosickỳ, and Sebastien Vasey. Forking independence from the categorical point of view. arXiv preprint arXiv:1801.09001, 2018. David Marker. Model theory: an introduction, volume 217. Springer Science & Business Media, 2006. Michael Makkai and Robert Paré. Accessible categories: the foundations of categorical model theory, volume 104. American Mathematical Soc., 1989. Michael 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. Anand Pillay. An introduction to stability theory. Courier Corporation, 2008. Saharon Shelah. Categoricity in א 1 of sentences in L , ω 1 ,ω (q). Israel Journal of Mathematics, 20(2):127–148, 1975. Saharon Shelah. Classification of non elementary classes ii abstract elementary classes. In Classification theory, pages 419–497. Springer, 1987. Saharon Shelah. Universal classes. In Classification theory, pages 264–418. Springer, 1987. Saharon Shelah. Cardinal arithmetic, volume 3. Oxford, 1994. Saharon Shelah. Categoricity for abstract classes with amalgamation. Annals of Pure and Applied Logic, 98(1-3):261–294, 1999. Saharon Shelah and Andrés Villaveces. Toward categoricity for classes with no maximal models. Annals of Pure and Applied Logic, 97(1-3):1–25, 1999. Saharon 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. Monica VanDieren. Categoricity in abstract elementary classes with no maximal models. Annals of Pure and Applied Logic, 141(1-2):108–147, 2006. Monica 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. Sebastien Vasey. Downward categoricity from a successor inside a good frame. Annals of Pure and Applied Logic, 168(3):651–692, 2017. Sebastien Vasey. Saturation and solvability in abstract elementary classes with amalgamation. Archive for Mathematical Logic, 56(5-6):671–690, 2017. Sebastien Vasey. Superstability and Categoricity in Abstract Elementary Classes. PhD thesis, Carnegie Mellon Unievrsity, 2017. Pedro Zambrano. Around superstability in metric abstract elementary classes. PhD thesis, Universidad Nacional de Colombia sede Bogotá, 2011. |
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CC0 1.0 Universalhttp://creativecommons.org/publicdomain/zero/1.0/Acceso abiertohttp://purl.org/coar/access_right/c_abf2Zambrano Ramirez, Pedro Hernánb206b56b-7b3b-4c1d-81e6-5c6939380547-1Nájar Salinas, José Nicolásc75b04ff-901a-49fa-a894-2bb11b5b2549Interacciones entre teoría de modelos, categorías, conjuntos y geometría algebraica2020-08-06T00:43:59Z2020-08-06T00:43:59Z2020-08-04https://repositorio.unal.edu.co/handle/unal/77951In 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.En 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.Línea de Investigación: Teoría de Modelos.nicolas.na7ar@gmail.comMaestría223application/pdfspa510 - Matemáticas516 - Geometría512 - ÁlgebraQ-abstract elementary classsuperstabilitysaturationshelah-Villaveces theoremQ-Clase Elemental Abstractasuperestabilidadteorema de Shelah-VillavecessaturaciónSobre la superestabilidad en Q-Clases elementales abstractasDocumento de trabajoinfo:eu-repo/semantics/workingPaperhttp://purl.org/coar/resource_type/c_8042Bogotá - Ciencias - Maestría en Ciencias - MatemáticasDepartamento de MatemáticasUniversidad Nacional de Colombia - Sede BogotáUri Abraham and Menachem Magidor. Cardinal arithmetic. In Handbook of set theory, pages 1149–1227. Springer, 2010.John T Baldwin. Ehrenfeucht-mostowski models in abstract elementary classes. Contemporary Mathematics, 380:1–16, 2005.John T Baldwin. Categoricity, volume 50. American Mathematical Soc., 2009.Will Boney and Rami Grossberg. Forking in short and tame abstract elementary classes. Annals of Pure and Applied Logic, 168(8):1517–1551, 2017.Will 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.John 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.Will Boney. Tameness from large cardinal axioms. The Journal of Symbolic Logic, 79(4):1092–1119, 2014.Tibor Beke and Jirí Rosickỳ. Abstract elementary classes and accessible categories. Annals of Pure and Applied Logic, 163(12):2008–2017, 2012.Will Boney and Sebastien Vasey. A survey on tame abstract elementary classes. arXiv preprint arXiv:1512.00060, 2015.Will Boney, Monica M VanDieren, and Sebastien Vasey. Shelah-villaveces revisited. arXiv preprint arXiv:1611.05292, 2016.Andrew H Coppola. The theory of Q-Abstract Elementary Classes. PhD thesis, University of Illinois at Chicago, 2006.Andrzej Ehrenfeucht and Andrzej Mostowski. Models of axiomatic theories admitting automorphisms. Fund. Math, 43:50–68, 1956.Christian Espíndola. A topos-theoretic proof of shelah’s eventual categoricity conjecture for abstract elementary classes. arXiv preprint arXiv:1906.09169, 2019.Rami Grossberg and Monica VanDieren. Galois-stability for tame abstract elementary classes. Journal of Mathematical Logic, 6(01):25–48, 2006.Rami Grossberg and Monica VanDieren. Shelah’s categoricity conjecture from a successor for tame abstract elementary classes. Journal of Symbolic Logic, pages 553–568, 2006.Rami Grossberg and Sebastien Vasey. Equivalent definitions of superstability in tame abstract elementary classes. The Journal of Symbolic Logic, 82(4):1387–1408, 2017.Rami Grossberg, Monica VanDieren, and Andrés Villaveces. Uniqueness of limit models in classes with amalgamation. Mathematical Logic Quarterly, 62(4-5):367–382, 2016.Thomas Jech. Set theory. the third millennium edition. Springer Monographs in Mathematics. Springer-Verlag, 2003.Olivier 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.Michael J Lieberman. Category-theoretic aspects of abstract elementary classes. Annals of Pure and Applied Logic, 162(11):903–915, 2011.Michael Lieberman and Jiri Rosicky. Approximations of superstability in concrete accessible categories. arXiv preprint arXiv:1505.06047, 2015.Michael Lieberman and Jirí Rosickỳ. Classification theory for accessible categories. The Journal of Symbolic Logic, 81(1):151–165, 2016.Michael Lieberman and Jirí Rosickỳ. Metric abstract elementary classes as accessible categories. The Journal of Symbolic Logic, 82(3):1022–1040, 2017.Michael Lieberman, Jiří Rosickỳ, and Sebastien Vasey. Forking independence from the categorical point of view. arXiv preprint arXiv:1801.09001, 2018.David Marker. Model theory: an introduction, volume 217. Springer Science & Business Media, 2006.Michael Makkai and Robert Paré. Accessible categories: the foundations of categorical model theory, volume 104. American Mathematical Soc., 1989.Michael 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.Anand Pillay. An introduction to stability theory. Courier Corporation, 2008.Saharon Shelah. Categoricity in א 1 of sentences in L , ω 1 ,ω (q). Israel Journal of Mathematics, 20(2):127–148, 1975.Saharon Shelah. Classification of non elementary classes ii abstract elementary classes. In Classification theory, pages 419–497. Springer, 1987.Saharon Shelah. Universal classes. In Classification theory, pages 264–418. Springer, 1987. Saharon Shelah. Cardinal arithmetic, volume 3. Oxford, 1994.Saharon Shelah. Categoricity for abstract classes with amalgamation. Annals of Pure and Applied Logic, 98(1-3):261–294, 1999.Saharon Shelah and Andrés Villaveces. Toward categoricity for classes with no maximal models. Annals of Pure and Applied Logic, 97(1-3):1–25, 1999.Saharon 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.Monica VanDieren. Categoricity in abstract elementary classes with no maximal models. Annals of Pure and Applied Logic, 141(1-2):108–147, 2006.Monica 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.Sebastien Vasey. Downward categoricity from a successor inside a good frame. Annals of Pure and Applied Logic, 168(3):651–692, 2017.Sebastien Vasey. Saturation and solvability in abstract elementary classes with amalgamation. Archive for Mathematical Logic, 56(5-6):671–690, 2017.Sebastien Vasey. Superstability and Categoricity in Abstract Elementary Classes. PhD thesis, Carnegie Mellon Unievrsity, 2017.Pedro Zambrano. Around superstability in metric abstract elementary classes. PhD thesis, Universidad Nacional de Colombia sede Bogotá, 2011.ORIGINALSobre la Superestabilidad en Q-Clases Elementales Abstractas.pdfSobre la Superestabilidad en Q-Clases Elementales Abstractas.pdfapplication/pdf1476578https://repositorio.unal.edu.co/bitstream/unal/77951/1/Sobre%20la%20Superestabilidad%20en%20Q-Clases%20Elementales%20Abstractas.pdfe1cf7d75b0760e3fdf203063b8befc6eMD51CC-LICENSElicense_rdflicense_rdfapplication/rdf+xml; charset=utf-8701https://repositorio.unal.edu.co/bitstream/unal/77951/3/license_rdf42fd4ad1e89814f5e4a476b409eb708cMD53LICENSElicense.txtlicense.txttext/plain; charset=utf-83895https://repositorio.unal.edu.co/bitstream/unal/77951/2/license.txte2f63a891b6ceb28c3078128251851bfMD52THUMBNAILSobre la Superestabilidad en Q-Clases Elementales Abstractas.pdf.jpgSobre la Superestabilidad en Q-Clases Elementales Abstractas.pdf.jpgGenerated 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