Constructible sets in lattice-valued models
We investigate different set-theoretic constructions in Residuated Logic based on Fitting’s work on Intuitionistic Kripke models of Set Theory. Firstly, we consider constructable sets within valued models of Set Theory. We present two distinct constructions of the constructable universe: L B and L B...
- Autores:
-
Moncayo Vega, Jose Ricardo
- Tipo de recurso:
- Fecha de publicación:
- 2023
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/83833
- Palabra clave:
- 510 - Matemáticas
Teoría de conjuntos
Set theory
Funciones de conjuntos
Set Functions
Algebra abstracta
Algebra, abstract
Valued models
Abstract logics
Residuated lattices
Kripke models
Constructible sets
Modelos valuados
Lógicas abstractas
Retículos residuales
Modelos de Kripke
Conjuntos construibles
- Rights
- openAccess
- License
- Atribución-NoComercial-SinDerivadas 4.0 Internacional
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| dc.title.eng.fl_str_mv |
Constructible sets in lattice-valued models |
| dc.title.translated.spa.fl_str_mv |
Conjuntos construibles en modelos valuados en retículos |
| title |
Constructible sets in lattice-valued models |
| spellingShingle |
Constructible sets in lattice-valued models 510 - Matemáticas Teoría de conjuntos Set theory Funciones de conjuntos Set Functions Algebra abstracta Algebra, abstract Valued models Abstract logics Residuated lattices Kripke models Constructible sets Modelos valuados Lógicas abstractas Retículos residuales Modelos de Kripke Conjuntos construibles |
| title_short |
Constructible sets in lattice-valued models |
| title_full |
Constructible sets in lattice-valued models |
| title_fullStr |
Constructible sets in lattice-valued models |
| title_full_unstemmed |
Constructible sets in lattice-valued models |
| title_sort |
Constructible sets in lattice-valued models |
| dc.creator.fl_str_mv |
Moncayo Vega, Jose Ricardo |
| dc.contributor.advisor.none.fl_str_mv |
Zambrano Ramírez, Pedro Hernán |
| dc.contributor.author.none.fl_str_mv |
Moncayo Vega, Jose Ricardo |
| dc.contributor.researchgroup.spa.fl_str_mv |
Interacciones Entre Teoría de Modelos, Teoría de Conjuntos, Categorías, Análisis y Geometría |
| dc.subject.ddc.spa.fl_str_mv |
510 - Matemáticas |
| topic |
510 - Matemáticas Teoría de conjuntos Set theory Funciones de conjuntos Set Functions Algebra abstracta Algebra, abstract Valued models Abstract logics Residuated lattices Kripke models Constructible sets Modelos valuados Lógicas abstractas Retículos residuales Modelos de Kripke Conjuntos construibles |
| dc.subject.lemb.none.fl_str_mv |
Teoría de conjuntos Set theory Funciones de conjuntos Set Functions Algebra abstracta Algebra, abstract |
| dc.subject.proposal.eng.fl_str_mv |
Valued models Abstract logics Residuated lattices Kripke models Constructible sets |
| dc.subject.proposal.spa.fl_str_mv |
Modelos valuados Lógicas abstractas Retículos residuales Modelos de Kripke Conjuntos construibles |
| description |
We investigate different set-theoretic constructions in Residuated Logic based on Fitting’s work on Intuitionistic Kripke models of Set Theory. Firstly, we consider constructable sets within valued models of Set Theory. We present two distinct constructions of the constructable universe: L B and L B , and prove that the they are isomorphic to V (von Neumann universe) and L (Gödel’s constructible universe), respectively. Secondly, we generalize Fitting’s work on Intuitionistic Kripke models of Set Theory using Ono and Komori’s Residuated Kripke models. Based on these models, we provide a general- ization of the von Neumann hierarchy in the context of Modal Residuated Logic and prove a translation of formulas between it and a suited Heyting valued model. We also propose a notion of universe of constructable sets in Modal Residuated Logic and discuss some aspects of it. |
| publishDate |
2023 |
| dc.date.accessioned.none.fl_str_mv |
2023-05-19T16:26:35Z |
| dc.date.available.none.fl_str_mv |
2023-05-19T16:26:35Z |
| dc.date.issued.none.fl_str_mv |
2023 |
| dc.type.spa.fl_str_mv |
Trabajo de grado - Maestría |
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info:eu-repo/semantics/masterThesis |
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info:eu-repo/semantics/acceptedVersion |
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Text |
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http://purl.org/redcol/resource_type/TM |
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acceptedVersion |
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https://repositorio.unal.edu.co/handle/unal/83833 |
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Universidad Nacional de Colombia |
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Repositorio Institucional Universidad Nacional de Colombia |
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https://repositorio.unal.edu.co/ |
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https://repositorio.unal.edu.co/handle/unal/83833 https://repositorio.unal.edu.co/ |
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Universidad Nacional de Colombia Repositorio Institucional Universidad Nacional de Colombia |
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eng |
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eng |
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Gerard Allwein and Wendy MacCaull, A Kripke Semantics for the Logic of Gelfand Quantales, Studia Logica 68 (2001), no. 2, 173–228. Gerard Allwein and Wendy MacCaull, A Kripke Semantics for the Logic of Gelfand Quantales, Studia Logica 68 (2001), no. 2, 173–228. Radim Belohlavek, Joseph W. Dauben, and George J. Klir, Fuzzy Logic and Mathematics: A Historical Perspective, 1 ed., Oxford University Press, New York, 2017 (eng). John L. Bell, Set Theory: Boolean-Valued Models and Independence Proofs, 3 ed., Oxford University Press UK, 2005. John Benavides N., La independencia de la hipótesis del continuo sobre un modelo fibrado para la teoría de conjuntos., 2004. Wim J. Blok and Don L. Pigozzi, Algebraizable Logics, vol. 77, American Math- ematical Society, Providence, 1989. Dumitru Buşneag and Dana Piciu, Some types of filters in residuated lattices, Soft Computing - A Fusion of Foundations, Methodologies and Applications 18 (2014), no. 5, 825–837. Xavier Caicedo, Lógica de los haces de estructuras., Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales XIX (1995), no. 74, 569– 585. Chen C. Chang, Sets constructible using Lκ,κ, Axiomatic Set Theory (Proc. Sym- pos. Pure Math. Vol. XIII (1971), 1–8. Robert P. Dilworth, Non-Commutative Residuated Lattices, Transactions of the American Mathematical Society 46 (1939), no. 3, 426–444. Brian A. Davey and Hilary A. Priestley, Introduction to Lattices and Order, 2 ed., Cambridge University Press, 2002. Michael Dummett, A Propositional Calculus with Denumerable Matrix, The Jour- nal of Symbolic Logic 24 (1959), no. 2, 97–106. Francesc Esteva and Lluís Godo, Monoidal t-norm Based Logic: Towards a Logic for Left-continuous t-norms., Fuzzy Sets and Systems 124 (2001), 271–288. Michael P. Fourman and Martin E. Hyland, Sheaf models for analysis, Appli- cations of Sheaves: Proceedings of the Research Symposium on Applications of Sheaf Theory to Logic, Algebra, and Analysis, Durham, July 9–21, 1977 (Michael Fourman, Christopher Mulvey, and Dana Scott, eds.), Springer Berlin Heidelberg, Berlin, Heidelberg, 1979, pp. 280–301. Melvin Fitting, Intuitionistic Logic, Model Theory and Forcing, 1 ed., North- Holland Pub. Co, Amsterdam, 1969. _______, Intuitionistic Model Theory and the Cohen Independence Proofs, Studies in Logic and the Foundations of Mathematics 60 (1970), no. C, 219–226. Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski, and Hiroakira Ono, Residuated lattices : an algebraic glimpse at substructural logics, 1 ed., vol. 151, Elsevier, Amsterdam, 2007. Kurt Gödel, Zum intuitionistischen aussagenkalkül, Anzeiger der Akademie der Wissenschaften in Wien, Mathematisch-naturwissenschaftliche Klasse 69 (1932), 65–66. _______, The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis, Proceedings of the National Academy of Sciences of the United States of America 24 (1938), no. 12, 556–557. Robin J. Grayson, Heyting-valued models for intuitionistic set theory, Applica- tions of Sheaves: Proceedings of the Research Symposium on Applications of Sheaf Theory to Logic, Algebra, and Analysis, Springer Berlin Heidelberg, 1979, pp. 402–414. Petr Hájek, Basic fuzzy logic and BL-algebras, Soft Computing 2 (1998), no. 3, 124–128. _____, Metamathematics of Fuzzy Logic, Trends in Logic, vol. 4, Springer Netherlands, Dordrecht, 1998. Petr Hájek and Zuzana Haniková, A set theory within fuzzy logic, Proceedings of The International Symposium on Multiple-Valued Logic (2001), 319–323. ______, A Development of Set Theory in Fuzzy Logic, Beyond Two: Theory and Applications of Multiple-Valued Logic, vol. 114, Physica Heidelberg, 1 ed., 2003, pp. 273–285. Ulrich Höhle, Monoidal Logic, Fuzzy-Systems in Computer Science, Vieweg+Teubner Verlag, 1994, pp. 233–243. ______, Commutative, residuated 1—monoids, Non-Classical Logics and their Applications to Fuzzy Subsets, Springer Netherlands, 1995, pp. 53–106. Thomas Jech, Set Theory, Springer Monographs in Mathematics, Springer Berlin Heidelberg, Berlin, Heidelberg, 2003. Juliette Kennedy, Menachem Magidor, and Jouko Väänänen, Inner Models from Extended Logics: Part 1, Avalaible at https://arxiv.org/pdf/2007.10764.pdf (2020). Saul A. Kripke, A completeness theorem in modal logic, Journal of Symbolic Logic 24 (1959), no. 1, 1–14. ______, Semantical Analysis of Intuitionistic Logic I, Formal Systems and Re- cursive Functions: Proceedings of the Eighth Logic Colloquium, Oxford July 1963 (Michael Dummett and John Crossley, eds.), no. 2, North Holland, 1963, pp. 92–130. _____, Semantical Analysis of Modal Logic I. Normal Propositional Calculi, Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (1963), no. 5-6, 67–96. Wolfgang Krull, Axiomatische Begründung der allgemeinen Ideal theorie, Sitzungsberichte der physikalisch medizinischen Societäd der Erlangen 56 (1924), 47–63. Kenneth Kunen, Set theory, College Publications, 2011. Kevin C. Lano, Fuzzy sets and residuated logic, Fuzzy Sets and Systems 47 (1992), no. 2, 203 – 220. _____, Set theoretic foundations for fuzzy set theory, and their applications, Log- ical Foundations of Computer Science — Tver ’92 (Berlin, Heidelberg) (Nerode Anil and Mikhail Taitslin, eds.), Springer Berlin Heidelberg, 1992, pp. 258–268. Wendy MacCaull, A note on Kripke semantics for residuated logic, Fuzzy Sets and Systems 77 (1996), no. 2, 229–234. Christopher Mulvey, &, Rendiconti del Circolo Matematico di Palermo 12 (1986), no. 2, 99–104. Hiroakira Ono and Yuichi Komori, Logics without the contraction rule, The Jour- nal of Symbolic Logic 50 (1985), no. 1, 169–201. Hiroakira Ono, Semantical analysis of predicate logics without the contraction rule, Studia Logica 44 (1985), no. 2, 187–196. ______, Substructural Logics and Residuated Lattices — an Introduction, Trends in Logic: 50 Years of Studia Logica, vol. 21, Springer, Dordrecht, 1 ed., 2003, pp. 193–228. Mitsuhiro Okada and Kazushige Terui, The finite model property for various fragments of intuitionistic linear logic, Journal of Symbolic Logic 64 (1999), no. 2, 790–802. Kimmo I. Rosenthal, Quantales and their applications, Longman Scientific & Technical, Essex, England, 1990. Helena Rasiowa and Roman Sikorski, The Mathematics of Metamathematics, Journal of Symbolic Logic 32 (1963), no. 2, 274–275. Dana Scott and John Myhill, Ordinal Definability, Axiomatic Set Theory: Pro- ceedings of Symposia in Pure Mathematics Vol. XIII (1971), 271–278. Dana Scott and Robert Solovay, Boolean-Valued Models for Set Theory, Mimeographed notes for the 1967 American Mathematical Society Symposium on axiomatic set theory, 1967. Parvin Safari and Saeed Salehi, Kripke semantics for fuzzy logics, Soft Computing 22 (2018), no. 3, 839–844. Dirk van Dalen, Logic and Structure, 4 ed., Springer Berlin, Heidelberg, 2004. Morgan Ward, Structure Residuation, Annals of Mathematics 39 (1938), no. 3, 558–568. Morgan Ward and Robert P. Dilworth, Residuated Lattices, Proceedings of the National Academy of Sciences of the United States of America 24 (1938), no. 3, 162–164. Frank Wolter and Michael Zakharyaschev, On the Blok-Esakia Theorem, Leo Esakia on Duality in Modal and Intuitionistic Logics, vol. 4, Springer, Dordrecht, 2014, pp. 99–118. Lotfi A. Zadeh, Fuzzy sets, Information and Control 8 (1965), no. 3, 338–353. Ernest Zermelo, Über Grenzzahlen und Mengenbereiche, Fundamenta Mathemat- icae 16 (1930), no. 1, 29–47 (ger). |
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Bogotá - Ciencias - Maestría en Ciencias - Matemáticas |
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Facultad de Ciencias |
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Atribución-NoComercial-SinDerivadas 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Zambrano Ramírez, Pedro Hernán81ad894ee4d503e5a9459e9ca6218ef3Moncayo Vega, Jose Ricardo967b9becc33001fc9afa2643e0641affInteracciones Entre Teoría de Modelos, Teoría de Conjuntos, Categorías, Análisis y Geometría2023-05-19T16:26:35Z2023-05-19T16:26:35Z2023https://repositorio.unal.edu.co/handle/unal/83833Universidad Nacional de ColombiaRepositorio Institucional Universidad Nacional de Colombiahttps://repositorio.unal.edu.co/We investigate different set-theoretic constructions in Residuated Logic based on Fitting’s work on Intuitionistic Kripke models of Set Theory. Firstly, we consider constructable sets within valued models of Set Theory. We present two distinct constructions of the constructable universe: L B and L B , and prove that the they are isomorphic to V (von Neumann universe) and L (Gödel’s constructible universe), respectively. Secondly, we generalize Fitting’s work on Intuitionistic Kripke models of Set Theory using Ono and Komori’s Residuated Kripke models. Based on these models, we provide a general- ization of the von Neumann hierarchy in the context of Modal Residuated Logic and prove a translation of formulas between it and a suited Heyting valued model. We also propose a notion of universe of constructable sets in Modal Residuated Logic and discuss some aspects of it.Investigamos diferentes construcciones de la teoría de conjuntos en Lógica Residual basados en el trabajo de Fitting sobre los modelos intuicionistas de Kripke de la Teoría de Conjuntos. En primer lugar, consideramos conjuntos construibles dentro de modelos valuados de la Teoría de Conjuntos. Presentamos dos construcciones distintas del universo construible: L B y L B , y demostramos que son isomorfos a V (universo von Neumann) y L (universo construible de Gödel), respectivamente. En segundo lugar, generalizamos el trabajo de Fitting sobre los modelos intuicionistas de Kripke de la teoría de conjuntos utilizando los modelos residuados de Kripke de Ono y Komori. Con base en estos modelos, proporcionamos una generalización de la jerarquía de von Neumann en el contexto de la Lógica Modal Residuada y demostramos una traducción de fórmulas entre ella y un modelo Heyting valuado adecuado. También proponemos una noción de universo de conjuntos construibles en Lógica Modal Residuada y discutimos algunos aspectos de la misma. (Texto tomado de la fuente)MaestríaMagíster en Ciencias - MatemáticasLógica matemática, teoría de conjuntosxviii, 166 páginasapplication/pdfengUniversidad Nacional de ColombiaBogotá - Ciencias - Maestría en Ciencias - MatemáticasFacultad de CienciasBogotá, ColombiaUniversidad Nacional de Colombia - Sede Bogotá510 - MatemáticasTeoría de conjuntosSet theoryFunciones de conjuntosSet FunctionsAlgebra abstractaAlgebra, abstractValued modelsAbstract logicsResiduated latticesKripke modelsConstructible setsModelos valuadosLógicas abstractasRetículos residualesModelos de KripkeConjuntos construiblesConstructible sets in lattice-valued modelsConjuntos construibles en modelos valuados en retículosTrabajo de grado - Maestríainfo:eu-repo/semantics/masterThesisinfo:eu-repo/semantics/acceptedVersionTexthttp://purl.org/redcol/resource_type/TMGerard Allwein and Wendy MacCaull, A Kripke Semantics for the Logic of Gelfand Quantales, Studia Logica 68 (2001), no. 2, 173–228.Gerard Allwein and Wendy MacCaull, A Kripke Semantics for the Logic of Gelfand Quantales, Studia Logica 68 (2001), no. 2, 173–228.Radim Belohlavek, Joseph W. Dauben, and George J. Klir, Fuzzy Logic and Mathematics: A Historical Perspective, 1 ed., Oxford University Press, New York, 2017 (eng).John L. Bell, Set Theory: Boolean-Valued Models and Independence Proofs, 3 ed., Oxford University Press UK, 2005.John Benavides N., La independencia de la hipótesis del continuo sobre un modelo fibrado para la teoría de conjuntos., 2004.Wim J. Blok and Don L. Pigozzi, Algebraizable Logics, vol. 77, American Math- ematical Society, Providence, 1989.Dumitru Buşneag and Dana Piciu, Some types of filters in residuated lattices, Soft Computing - A Fusion of Foundations, Methodologies and Applications 18 (2014), no. 5, 825–837.Xavier Caicedo, Lógica de los haces de estructuras., Revista de la Academia Colombiana de Ciencias Exactas, Físicas y Naturales XIX (1995), no. 74, 569– 585.Chen C. Chang, Sets constructible using Lκ,κ, Axiomatic Set Theory (Proc. Sym- pos. Pure Math. Vol. XIII (1971), 1–8.Robert P. Dilworth, Non-Commutative Residuated Lattices, Transactions of the American Mathematical Society 46 (1939), no. 3, 426–444.Brian A. Davey and Hilary A. Priestley, Introduction to Lattices and Order, 2 ed., Cambridge University Press, 2002.Michael Dummett, A Propositional Calculus with Denumerable Matrix, The Jour- nal of Symbolic Logic 24 (1959), no. 2, 97–106.Francesc Esteva and Lluís Godo, Monoidal t-norm Based Logic: Towards a Logic for Left-continuous t-norms., Fuzzy Sets and Systems 124 (2001), 271–288.Michael P. Fourman and Martin E. Hyland, Sheaf models for analysis, Appli- cations of Sheaves: Proceedings of the Research Symposium on Applications of Sheaf Theory to Logic, Algebra, and Analysis, Durham, July 9–21, 1977 (Michael Fourman, Christopher Mulvey, and Dana Scott, eds.), Springer Berlin Heidelberg, Berlin, Heidelberg, 1979, pp. 280–301.Melvin Fitting, Intuitionistic Logic, Model Theory and Forcing, 1 ed., North- Holland Pub. Co, Amsterdam, 1969._______, Intuitionistic Model Theory and the Cohen Independence Proofs, Studies in Logic and the Foundations of Mathematics 60 (1970), no. C, 219–226.Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski, and Hiroakira Ono, Residuated lattices : an algebraic glimpse at substructural logics, 1 ed., vol. 151, Elsevier, Amsterdam, 2007.Kurt Gödel, Zum intuitionistischen aussagenkalkül, Anzeiger der Akademie der Wissenschaften in Wien, Mathematisch-naturwissenschaftliche Klasse 69 (1932), 65–66._______, The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis, Proceedings of the National Academy of Sciences of the United States of America 24 (1938), no. 12, 556–557.Robin J. Grayson, Heyting-valued models for intuitionistic set theory, Applica- tions of Sheaves: Proceedings of the Research Symposium on Applications of Sheaf Theory to Logic, Algebra, and Analysis, Springer Berlin Heidelberg, 1979, pp. 402–414.Petr Hájek, Basic fuzzy logic and BL-algebras, Soft Computing 2 (1998), no. 3, 124–128._____, Metamathematics of Fuzzy Logic, Trends in Logic, vol. 4, Springer Netherlands, Dordrecht, 1998.Petr Hájek and Zuzana Haniková, A set theory within fuzzy logic, Proceedings of The International Symposium on Multiple-Valued Logic (2001), 319–323.______, A Development of Set Theory in Fuzzy Logic, Beyond Two: Theory and Applications of Multiple-Valued Logic, vol. 114, Physica Heidelberg, 1 ed., 2003, pp. 273–285.Ulrich Höhle, Monoidal Logic, Fuzzy-Systems in Computer Science, Vieweg+Teubner Verlag, 1994, pp. 233–243.______, Commutative, residuated 1—monoids, Non-Classical Logics and their Applications to Fuzzy Subsets, Springer Netherlands, 1995, pp. 53–106.Thomas Jech, Set Theory, Springer Monographs in Mathematics, Springer Berlin Heidelberg, Berlin, Heidelberg, 2003.Juliette Kennedy, Menachem Magidor, and Jouko Väänänen, Inner Models from Extended Logics: Part 1, Avalaible at https://arxiv.org/pdf/2007.10764.pdf (2020).Saul A. Kripke, A completeness theorem in modal logic, Journal of Symbolic Logic 24 (1959), no. 1, 1–14.______, Semantical Analysis of Intuitionistic Logic I, Formal Systems and Re- cursive Functions: Proceedings of the Eighth Logic Colloquium, Oxford July 1963 (Michael Dummett and John Crossley, eds.), no. 2, North Holland, 1963, pp. 92–130._____, Semantical Analysis of Modal Logic I. Normal Propositional Calculi, Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 9 (1963), no. 5-6, 67–96.Wolfgang Krull, Axiomatische Begründung der allgemeinen Ideal theorie, Sitzungsberichte der physikalisch medizinischen Societäd der Erlangen 56 (1924), 47–63.Kenneth Kunen, Set theory, College Publications, 2011.Kevin C. Lano, Fuzzy sets and residuated logic, Fuzzy Sets and Systems 47 (1992), no. 2, 203 – 220._____, Set theoretic foundations for fuzzy set theory, and their applications, Log- ical Foundations of Computer Science — Tver ’92 (Berlin, Heidelberg) (Nerode Anil and Mikhail Taitslin, eds.), Springer Berlin Heidelberg, 1992, pp. 258–268.Wendy MacCaull, A note on Kripke semantics for residuated logic, Fuzzy Sets and Systems 77 (1996), no. 2, 229–234.Christopher Mulvey, &, Rendiconti del Circolo Matematico di Palermo 12 (1986), no. 2, 99–104.Hiroakira Ono and Yuichi Komori, Logics without the contraction rule, The Jour- nal of Symbolic Logic 50 (1985), no. 1, 169–201.Hiroakira Ono, Semantical analysis of predicate logics without the contraction rule, Studia Logica 44 (1985), no. 2, 187–196.______, Substructural Logics and Residuated Lattices — an Introduction, Trends in Logic: 50 Years of Studia Logica, vol. 21, Springer, Dordrecht, 1 ed., 2003, pp. 193–228.Mitsuhiro Okada and Kazushige Terui, The finite model property for various fragments of intuitionistic linear logic, Journal of Symbolic Logic 64 (1999), no. 2, 790–802.Kimmo I. Rosenthal, Quantales and their applications, Longman Scientific & Technical, Essex, England, 1990.Helena Rasiowa and Roman Sikorski, The Mathematics of Metamathematics, Journal of Symbolic Logic 32 (1963), no. 2, 274–275.Dana Scott and John Myhill, Ordinal Definability, Axiomatic Set Theory: Pro- ceedings of Symposia in Pure Mathematics Vol. XIII (1971), 271–278.Dana Scott and Robert Solovay, Boolean-Valued Models for Set Theory, Mimeographed notes for the 1967 American Mathematical Society Symposium on axiomatic set theory, 1967.Parvin Safari and Saeed Salehi, Kripke semantics for fuzzy logics, Soft Computing 22 (2018), no. 3, 839–844.Dirk van Dalen, Logic and Structure, 4 ed., Springer Berlin, Heidelberg, 2004.Morgan Ward, Structure Residuation, Annals of Mathematics 39 (1938), no. 3, 558–568.Morgan Ward and Robert P. Dilworth, Residuated Lattices, Proceedings of the National Academy of Sciences of the United States of America 24 (1938), no. 3, 162–164.Frank Wolter and Michael Zakharyaschev, On the Blok-Esakia Theorem, Leo Esakia on Duality in Modal and Intuitionistic Logics, vol. 4, Springer, Dordrecht, 2014, pp. 99–118.Lotfi A. Zadeh, Fuzzy sets, Information and Control 8 (1965), no. 3, 338–353.Ernest Zermelo, Über Grenzzahlen und Mengenbereiche, Fundamenta Mathemat- icae 16 (1930), no. 1, 29–47 (ger).LICENSElicense.txtlicense.txttext/plain; charset=utf-85879https://repositorio.unal.edu.co/bitstream/unal/83833/1/license.txteb34b1cf90b7e1103fc9dfd26be24b4aMD51ORIGINAL1014286254.2023 - Jose Ricardo Moncayo Vega.pdf1014286254.2023 - Jose Ricardo Moncayo Vega.pdfTesis de Maestría en Ciencias - Matemáticasapplication/pdf887203https://repositorio.unal.edu.co/bitstream/unal/83833/2/1014286254.2023%20-%20Jose%20Ricardo%20Moncayo%20Vega.pdfafdcfa4f25ca719e08b1525cfe41a65dMD52THUMBNAIL1014286254.2023 - Jose Ricardo Moncayo Vega.pdf.jpg1014286254.2023 - Jose Ricardo Moncayo Vega.pdf.jpgGenerated 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