On a question about families of entire functionsAll (original) (raw)

Tom 239 / 2017

Fundamenta Mathematicae 239 (2017), 279-288 MSC: Primary 03E35; Secondary 03E75. DOI: 10.4064/fm252-3-2017 Opublikowany online: 28 April 2017

Streszczenie

We show that the existence of a continuum sized family mathcalF\mathcal {F}mathcalF of entire functions such that for each complex number zzz, the set f(z):finmathcalF\{ f(z) : f \in \mathcal {F}\}f(z):finmathcalF has size less than continuum is undecidable in ZFC plus the negation of CH.

Autorzy

• Ashutosh KumarEinstein Institute of Mathematics
  The Hebrew University of Jerusalem
  Edmond J Safra Campus
  Givat Ram
  Jerusalem 91904, Israel
  e-mail
• Saharon ShelahEinstein Institute of Mathematics
  The Hebrew University of Jerusalem
  Edmond J Safra Campus
  Givat Ram
  Jerusalem 91904, Israel
  and
  Department of Mathematics
  Rutgers, The State University of New Jersey
  Hill Center, Busch Campus
  110 Frelinghuysen Road
  Piscataway, NJ 08854-8019, U.S.A.
  e-mail