Absoluteness theorems for arbitrary Polish spaces

Diego Alejandro Mejía; Ismael E. Rivera-Madrid

doi:10.15446/recolma.v53n2.85521

Published

2019-07-01

Absoluteness theorems for arbitrary Polish spaces

Teoremas de absolutidad para espacios polacos arbitrarios

DOI:

https://doi.org/10.15446/recolma.v53n2.85521

Keywords:

Mostowski's Absoluteness Theorem, Shoenfield's Absoluteness Theorem, Polish metric spaces (en)
Teorema de Absolutidad de Mostowski, Teorema de Absolutidad de Shoenfield, espacios métricos polacos (es)

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Authors

Diego Alejandro Mejía Shizuoka University
Ismael E. Rivera-Madrid Institución Universitaria Pascual Bravo

Abstract (en)
Abstract (es)

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.

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 clásico Teorema de Absolutidad (para conjuntos analíticos) de Mostowski para cualquier espacio métrico polaco en general. Adicionalmente, probamos una versión general del Teorema de Absolutidad de Shoenfield.

References

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How to Cite

APA

Mejía, D. A. and Rivera-Madrid, I. E. (2019). Absoluteness theorems for arbitrary Polish spaces. Revista Colombiana de Matemáticas, 53(2), 109–123. https://doi.org/10.15446/recolma.v53n2.85521

ACM

[1]

Mejía, D.A. and Rivera-Madrid, I.E. 2019. Absoluteness theorems for arbitrary Polish spaces. Revista Colombiana de Matemáticas. 53, 2 (Jul. 2019), 109–123. DOI:https://doi.org/10.15446/recolma.v53n2.85521.

ACS

(1)

Mejía, D. A.; Rivera-Madrid, I. E. Absoluteness theorems for arbitrary Polish spaces. rev.colomb.mat 2019, 53, 109-123.

ABNT

MEJÍA, D. A.; RIVERA-MADRID, I. E. Absoluteness theorems for arbitrary Polish spaces. Revista Colombiana de Matemáticas, [S. l.], v. 53, n. 2, p. 109–123, 2019. DOI: 10.15446/recolma.v53n2.85521. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/85521. Acesso em: 22 jan. 2025.

Chicago

Mejía, Diego Alejandro, and Ismael E. Rivera-Madrid. 2019. “Absoluteness theorems for arbitrary Polish spaces”. Revista Colombiana De Matemáticas 53 (2):109-23. https://doi.org/10.15446/recolma.v53n2.85521.

Harvard

Mejía, D. A. and Rivera-Madrid, I. E. (2019) “Absoluteness theorems for arbitrary Polish spaces”, Revista Colombiana de Matemáticas, 53(2), pp. 109–123. doi: 10.15446/recolma.v53n2.85521.

IEEE

[1]

D. A. Mejía and I. E. Rivera-Madrid, “Absoluteness theorems for arbitrary Polish spaces”, rev.colomb.mat, vol. 53, no. 2, pp. 109–123, Jul. 2019.

MLA

Mejía, D. A., and I. E. Rivera-Madrid. “Absoluteness theorems for arbitrary Polish spaces”. Revista Colombiana de Matemáticas, vol. 53, no. 2, July 2019, pp. 109-23, doi:10.15446/recolma.v53n2.85521.

Turabian

Mejía, Diego Alejandro, and Ismael E. Rivera-Madrid. “Absoluteness theorems for arbitrary Polish spaces”. Revista Colombiana de Matemáticas 53, no. 2 (July 1, 2019): 109–123. Accessed January 22, 2025. https://revistas.unal.edu.co/index.php/recolma/article/view/85521.

Vancouver

1.

Mejía DA, Rivera-Madrid IE. Absoluteness theorems for arbitrary Polish spaces. rev.colomb.mat [Internet]. 2019 Jul. 1 [cited 2025 Jan. 22];53(2):109-23. Available from: https://revistas.unal.edu.co/index.php/recolma/article/view/85521