Hilbert spaces with generic predicates
We study the model theory of expansions of Hilbert spaces by generic predicates. We first prove the existence of model companions for generic expansions of Hilbert spaces in the form of a distance function to a random substructure, then a distance to a random subset. The theory obtained with the ran...
- Autores:
-
Berenstein, Alexander
Hyttinen, Tapani
Villaveces, Andrés
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2018
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/66427
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/66427
http://bdigital.unal.edu.co/67455/
- Palabra clave:
- 51 Matemáticas / Mathematics
Continuous logic
Random Predicates
TP2
Stability theory
Lógica continua
Predicados aleatorios
TP2
Estabilidad
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Berenstein, Alexanderd8c7229e-81ea-458f-90c5-5d6605e80ce9300Hyttinen, Tapanif9795828-40f0-4471-8ca7-09dc3df5c25e300Villaveces, Andrésbac3f190-19d8-4627-8dc0-176b75165cd83002019-07-03T02:06:27Z2019-07-03T02:06:27Z2018-01-01ISSN: 2357-4100https://repositorio.unal.edu.co/handle/unal/66427http://bdigital.unal.edu.co/67455/We study the model theory of expansions of Hilbert spaces by generic predicates. We first prove the existence of model companions for generic expansions of Hilbert spaces in the form of a distance function to a random substructure, then a distance to a random subset. The theory obtained with the random substructure is ω-stable, while the one obtained with the distance to a random subset is TP2 and NSOP1. That example is the first continuous structure in that class.Estudiamos la teoría de modelos de expansiones de espacios de Hilbert mediante predicados genéricos. Primero demostramos la existencia de modelo-compañeras de expansiones genéricas de espacios de Hilbert mediante una función-distancia a una estructura aleatoria, y luego una distancia a un subconjunto aleatorio. La teoría obtenida con la subestructura aleatoria es ω-estable; la obtenida mediante la distancia a subconjunto aleatorio es TP2 y NSOP1. Este ejemplo es la primera estructura de esta clase de complejidad en lógica continua.application/pdfspaUniversidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticashttps://revistas.unal.edu.co/index.php/recolma/article/view/74566Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasBerenstein, Alexander and Hyttinen, Tapani and Villaveces, Andrés (2018) Hilbert spaces with generic predicates. Revista Colombiana de Matemáticas, 52 (1). pp. 107-130. ISSN 2357-410051 Matemáticas / MathematicsContinuous logicRandom PredicatesTP2Stability theoryLógica continuaPredicados aleatoriosTP2EstabilidadHilbert spaces with generic predicatesArtículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTORIGINAL74566-395570-1-SM.pdfapplication/pdf530856https://repositorio.unal.edu.co/bitstream/unal/66427/1/74566-395570-1-SM.pdf0ccb5e220d88518101f0a8635a8bec66MD51THUMBNAIL74566-395570-1-SM.pdf.jpg74566-395570-1-SM.pdf.jpgGenerated Thumbnailimage/jpeg5199https://repositorio.unal.edu.co/bitstream/unal/66427/2/74566-395570-1-SM.pdf.jpgc3d1a5cc20854a619b162c54b2e0600dMD52unal/66427oai:repositorio.unal.edu.co:unal/664272024-05-16 23:09:22.527Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
Hilbert spaces with generic predicates |
| title |
Hilbert spaces with generic predicates |
| spellingShingle |
Hilbert spaces with generic predicates 51 Matemáticas / Mathematics Continuous logic Random Predicates TP2 Stability theory Lógica continua Predicados aleatorios TP2 Estabilidad |
| title_short |
Hilbert spaces with generic predicates |
| title_full |
Hilbert spaces with generic predicates |
| title_fullStr |
Hilbert spaces with generic predicates |
| title_full_unstemmed |
Hilbert spaces with generic predicates |
| title_sort |
Hilbert spaces with generic predicates |
| dc.creator.fl_str_mv |
Berenstein, Alexander Hyttinen, Tapani Villaveces, Andrés |
| dc.contributor.author.spa.fl_str_mv |
Berenstein, Alexander Hyttinen, Tapani Villaveces, Andrés |
| dc.subject.ddc.spa.fl_str_mv |
51 Matemáticas / Mathematics |
| topic |
51 Matemáticas / Mathematics Continuous logic Random Predicates TP2 Stability theory Lógica continua Predicados aleatorios TP2 Estabilidad |
| dc.subject.proposal.spa.fl_str_mv |
Continuous logic Random Predicates TP2 Stability theory Lógica continua Predicados aleatorios TP2 Estabilidad |
| description |
We study the model theory of expansions of Hilbert spaces by generic predicates. We first prove the existence of model companions for generic expansions of Hilbert spaces in the form of a distance function to a random substructure, then a distance to a random subset. The theory obtained with the random substructure is ω-stable, while the one obtained with the distance to a random subset is TP2 and NSOP1. That example is the first continuous structure in that class. |
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2018 |
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2018-01-01 |
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2019-07-03T02:06:27Z |
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2019-07-03T02:06:27Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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info:eu-repo/semantics/publishedVersion |
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http://purl.org/coar/resource_type/c_6501 |
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ISSN: 2357-4100 |
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https://repositorio.unal.edu.co/handle/unal/66427 |
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http://bdigital.unal.edu.co/67455/ |
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ISSN: 2357-4100 |
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https://repositorio.unal.edu.co/handle/unal/66427 http://bdigital.unal.edu.co/67455/ |
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spa |
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spa |
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https://revistas.unal.edu.co/index.php/recolma/article/view/74566 |
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Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas |
| dc.relation.references.spa.fl_str_mv |
Berenstein, Alexander and Hyttinen, Tapani and Villaveces, Andrés (2018) Hilbert spaces with generic predicates. Revista Colombiana de Matemáticas, 52 (1). pp. 107-130. ISSN 2357-4100 |
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Derechos reservados - Universidad Nacional de Colombia |
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Atribución-NoComercial 4.0 Internacional |
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http://creativecommons.org/licenses/by-nc/4.0/ |
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info:eu-repo/semantics/openAccess |
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Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2 |
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Universidad Nacional de Colombia - Sede Bogotá - Facultad de Ciencias - Departamento de Matemáticas - Sociedad Colombiana de Matemáticas |
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