A model with no magic sets
Logic
2016-09-07 v1
Abstract
We will prove that there exists a model of ZFC+``c= omega_2'' in which every M subseteq R of cardinality less than continuum c is meager, and such that for every X subseteq R of cardinality c there exists a continuous function f:R-> R with f[X]=[0,1]. In particular in this model there is no magic set, i.e., a set M subseteq R such that the equation f[M]=g[M] implies f=g for every continuous nowhere constant functions f,g:R-> R .
Keywords
Cite
@article{arxiv.math/9801154,
title = {A model with no magic sets},
author = {Krzysztof Ciesielski and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9801154},
year = {2016}
}