## Journal of Symbolic Logic

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

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

#### 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

**Permanent link to this document**

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

**Mathematical Reviews number (MathSciNet)**

MR1456106

**Zentralblatt MATH identifier**

0877.20037

**JSTOR**

links.jstor.org

#### Citation

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