PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On a question about families of entire functions

Volume 239 / 2017

Ashutosh Kumar, Saharon Shelah 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.

Authors

  • 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

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image