Abstract:We provide answers to a question brought up by Erdős about the construction of Wetzel families in the absence of the continuum hypothesis: A Wetzel family is a family of entire functions on the complex plane which pointwise assumes fewer than values. To be more precise, we show that the existence of a Wetzel family is consistent with all possible values of the continuum and, if is regular, also with Martin's Axiom. In the particular case of this answers the main open question asked by Kumar and Shelah [Fu… Show more
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