On a question about families of entire functions
Volume 239 / 2017
Fundamenta Mathematicae 239 (2017), 279-288
MSC: Primary 03E35; Secondary 03E75.
DOI: 10.4064/fm252-3-2017
Published online: 28 April 2017
Abstract
We show that the existence of a continuum sized family $\mathcal {F}$ of entire functions such that for each complex number $z$, the set $\{ f(z) : f \in \mathcal {F}\}$ has size less than continuum is undecidable in ZFC plus the negation of CH.
