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Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
Rev.colomb.mat. vol.52 no.1 Bogotá Jan./June 2018
https://doi.org/10.15446/recolma.v1n52.74566
Original articles
Hilbert spaces with generic predicates
Espacios de Hilbert con predicados genéricos
1 Universidad de Los Andes, Bogotá- Colombia
2 University of Helsinki, Helsinki - Finland
3 Universidad Nacional de Colombia, Bogotá - Colombia
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 (-stable, while the one obtained with the distance to a random subset is TP 2 and NSOP 1. That example is the first continuous structure in that class.
Keywords: Continuous logic; Random Predicates; TP 2; Stability theory
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 (-estable; la obtenida mediante la distancia a subconjunto aleatorio es TP 2 y NSOP 1. Este ejemplo es la primera estructura de esta clase de complejidad en lógica continua.
Palabras clave: Lógica continua; Predicados aleatorios; TP 2; Estabilidad
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Received: March 06, 2017; Accepted: January 06, 2018