Open AccessAbsoluteness theorems for arbitrary Polish spaces
Author(s) -
Diego Mejía,
Ismael E. Rivera-Madrid
Publication year - 2019
Publication title -
revista colombiana de matemáticas/revista colombiana de matematicas
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.176
H-Index - 7
eISSN - 2357-4100
pISSN - 0034-7426
DOI - 10.15446/recolma.v53n2.85521
Subject(s) - absoluteness , mathematics , metric space , countable set , pure mathematics , polish space , metric (unit) , discrete mathematics , mathematical analysis , computer science , operations management , separable space , economics , programming language
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.