A model with no magic sets
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 .
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 1998
 DOI:
 10.48550/arXiv.math/9801154
 arXiv:
 arXiv:math/9801154
 Bibcode:
 1998math......1154C
 Keywords:

 Mathematics  Logic