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

Shelah, Saharon

Shelah, Saharon

J. Symbolic Logic, Tome 61 (1996) no. 1, p. 1261-1278 / Harvested from Project Euclid

Résumé

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.

Publié le : 1996-12-14
Classification:

@article{1183745134,
     author = {Shelah, Saharon},
     title = {If There is an Exactly $\lambda$-Free Abelian Group Then There is an Exactly $\lambda$-Separable one in $\lambda$},
     journal = {J. Symbolic Logic},
     volume = {61},
     number = {1},
     year = {1996},
     pages = { 1261-1278},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745134}
}

Shelah, Saharon. If There is an Exactly $\lambda$-Free Abelian Group Then There is an Exactly $\lambda$-Separable one in $\lambda$. J. Symbolic Logic, Tome 61 (1996) no. 1, pp.  1261-1278. http://gdmltest.u-ga.fr/item/1183745134/