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Revista Colombiana de Matemáticas
versión impresa ISSN 0034-7426
Rev.colomb.mat. vol.53 no.2 Bogotá jul./dic. 2019 Epub 20-Mar-2020
Artículos originales
Absoluteness theorems for arbitrary Polish spaces
Teoremas de absolutidad para espacios polacos arbitrarios
1Shizuoka University, Shizuoka, Japan. Faculty of Science Smzuok A University 836 Ohya, Suruga-ku, 422-8529 Shizuoka, Japan e-mail: diego.mejia@shizuoka.ac.jp
2Institución Universitaria Pascual Bravo, Medellín, Colombia. Faculty of Engineering Institución Universitaria Pascual Bravo Calle 73 No. 73A - 226 Medellín, Colombia e-mail: ismael.rivera@pascualbravo.edu.co
By coding Polish metric spaces with metrics on countable sets, we propose an interpretation of Polish metric spaces in models of ZFC and extend Mostowski's classical theorem of absoluteness of analytic sets for any Polish metric space in general. In addition, we prove a general version of Shoenfield's absoluteness theorem.
Key words and phrases. Mostowski's Absoluteness Theorem; Shoenfield's Absoluteness Theorem; Polish metric spaces
Mediante la codificación de espacios polacos con métricas de conjuntos contables, proponemos una interpretación de espacios métricos polacos en modelos de ZFC y extendemos el clósico Teorema de Absolutidad (para conjuntos analíticos) de Mostowski para cualquier espacio métrico polaco en general. Adicionalmente, probamos una versioón general del Teorema de Absolutidad de Shoenfield.
Palabras y frases clave. Teorema de Absolutidad de Mostowski; Teorema de Absolutidad de Shoenfield; espacios metricos polacos
Acknowledgements.
The first author is supported by Grant-in-Aid 18K13448 for Early Career Scientists, Japan Society for the Promotion of Science. Both authors are supported by the grant no. IN201711, Dirección Operativa de Investigación, Institución Universitaria Pascual Bravo.
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Received: February 2018; Accepted: February 2019
Todo el contenido de esta revista, excepto dónde está identificado, está bajo una Licencia Creative Commons BY
