## Journal of Symbolic Logic

### If There is an Exactly $\lambda$-Free Abelian Group Then There is an Exactly $\lambda$-Separable one in $\lambda$

Saharon Shelah

#### Abstract

We give a solution stated in the title to problem 3 of part 1 of the problems listed in the book of Eklof and Mekler [2], p. 453. There, in pp. 241-242, this is discussed and proved in some cases. The existence of strongly $\lambda$-free ones was proved earlier by the criteria in [5] and [3]. We can apply a similar proof to a large class of other varieties in particular to the variety of (non-commutative) groups.

#### Article information

Source
J. Symbolic Logic, Volume 61, Issue 4 (1996), 1261-1278.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183745134

Mathematical Reviews number (MathSciNet)
MR1456106

Zentralblatt MATH identifier
0877.20037

JSTOR
Shelah, Saharon. If There is an Exactly $\lambda$-Free Abelian Group Then There is an Exactly $\lambda$-Separable one in $\lambda$. J. Symbolic Logic 61 (1996), no. 4, 1261--1278. https://projecteuclid.org/euclid.jsl/1183745134