### Decompositions of reflexive modules

by Goebel and Shelah. [GbSh:716]

Archiv der Math, 2001

We continue [GbSh:568], proving a stronger result under the
special continuum hypothesis (CH). The original question of Eklof
and Mekler related to dual abelian groups. We want to find a
particular example of a dual group, which will provide a negative
answer to the question. In order to derive a stronger and also
more
general result we will concentrate on reflexive modules over
countable principal ideal domains R . Following H.~Bass, an
R-module G is reflexive if the evaluation map
sigma :G ---> G^{**} is an isomorphism. Here G^*= Hom (G,R) denotes
the dual group of G . Guided by classical
results the question about the existence of a reflexive R-module
G of infinite rank with G not cong G oplus R is natural. We will
use a theory of bilinear forms on free R-modules which strengthens
our algebraic results in [GbSh:568]. Moreover we want to apply a
model theoretic combinatorial theorem from [Sh:e] which allows us to
avoid the weak diamond principle. This has the great advantage that
the used prediction principle is still similar to the diamond, but
holds under CH.

Back to the list of publications