NÉ´-free abelian group with no non-zero homomorphism to â„¤

Saharon Shelah

NÉ´-free abelian group with no non-zero homomorphism to â„¤

Authors

Saharon Shelah The Hebrew University of Jerusalem, Einstein Institute of Mathematics Edmond J. Safra Campus, Givat Ram Jerusalem 91904, Israel.

Keywords:

Abelian groups, freeness, few homomorphism, set theory, black box

Abstract

We, far any natural ð‘›, construct an N_ð‘›-free abelian groups which have few homomorphisms to â„¤. For this we use "N_ð‘›-free (ð‘› + 1)-dimensional black boxes". The method is hopefully relevant to other constructions of N_ð‘›-free abelian groups.