# Sh:653

• Ciesielski, K. C., & Shelah, S. (1999). A model with no magic set. J. Symbolic Logic, 64(4), 1467–1490.
• Abstract:
We will prove that there exists a model of ZFC+“\mathfrak{c}=\omega_2” in which every M\subseteq R of cardinality less than continuum \mathfrak{c} is meager, and such that for every X\subseteq R of cardinality \mathfrak{c} there exists a continuous function f:R\to 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\to R.
• Version 1998-01-28_11 (33p) published version (25p)
Bib entry
@article{Sh:653,
author = {Ciesielski, Krzysztof Chris and Shelah, Saharon},
title = {{A model with no magic set}},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {64},
number = {4},
year = {1999},
pages = {1467--1490},
issn = {0022-4812},
mrnumber = {1780064},
mrclass = {03E35 (03E17)},
doi = {10.2307/2586790},
note = {\href{https://arxiv.org/abs/math/9801154}{arXiv: math/9801154}},
arxiv_number = {math/9801154}
}