# Sh:653

- Ciesielski, K. C., & Shelah, S. (1999).
*A model with no magic set*. J. Symbolic Logic,**64**(4), 1467–1490. arXiv: math/9801154 DOI: 10.2307/2586790 MR: 1780064 -
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. - 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}, doi = {10.2307/2586790}, mrclass = {03E35 (03E17)}, mrnumber = {1780064}, mrreviewer = {P\'eter Komj\'ath}, doi = {10.2307/2586790}, note = {\href{https://arxiv.org/abs/math/9801154}{arXiv: math/9801154}}, arxiv_number = {math/9801154} }