نبذة مختصرة : 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.
Relation: https://revistas.unal.edu.co/index.php/recolma/article/view/85521/74104; Miguel A. Cardona and Diego A. Mejía, On cardinal characteristics of Yorioka ideals, Math. Log. Quart. 65 (2019), no. 2, 170-199. [2] John D. Clemens, Isometry of Polish metric spaces, Ann. Pure Appl. Logic 163 (2012), no. 9, 1196-1209. MR 2926279 [3] Su Gao, Invariant descriptive set theory, Pure and Applied Mathematics (Boca Raton), vol. 293, CRC Press, Boca Raton, FL, 2009. MR 2455198 [4] Thomas Jech, Set theory, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003, The third millennium edition, revised and expanded. MR 1940513 (2004g:03071) [5] Alexander S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995. MR 1321597 (96e:03057) [6] S. C. Kleene, On the forms of the predicates in the theory of constructive ordinals. II, Amer. J. Math. 77 (1955), 405-428. MR 0070595 [7] Diego A. Mejía, Coding polish spaces, Kyoto Daigaku Surikaiseki Kenkyusho Kokyuroku (2017), no. 2050, 153-161. [8] Yiannis N. Moschovakis, Descriptive set theory, second ed., Mathematical Surveys and Monographs, vol. 155, American Mathematical Society, Providence, RI, 2009. MR 2526093 [9] A. Mostowski, A class of models for second order arithmetic, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astr. Phys. 7 (1959), 401-404. (unbound insert). MR 0115908 [10] J. R. Shoenfield, The problem of predicativity, Essays on the foundations of mathematics, Magnes Press, Hebrew Univ., Jerusalem, 1961, pp. 132-139. MR 0164886 [11] Robert M. Solovay, A model of set-theory in which every set of reals is Lebesgue measurable, Ann. of Math. (2) 92 (1970), 1-56. MR 0265151; https://revistas.unal.edu.co/index.php/recolma/article/view/85521
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