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If there is an exactly λ-free abelian group then there is an exactly λ-separable one in λ

Published online by Cambridge University Press:  12 March 2014

Saharon Shelah*
Institute of Mathematics, The Hebrew University, Jerusalem, Israel Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903, USA


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 λ-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.

Research Article
Copyright © Association for Symbolic Logic 1996

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