Decompositions of Reflexive Modules
Abstract
We continue [GbSh:568] (math.LO/0003164), 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 Rmodule G is reflexive if the evaluation map s: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 Rmodule G of infinite rank with G not cong G+R is natural. We will use a theory of bilinear forms on free Rmodules which strengthens our algebraic results in [GbSh:568] (math.LO/0003164). 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2000
 arXiv:
 arXiv:math/0003165
 Bibcode:
 2000math......3165G
 Keywords:

 Logic;
 Group Theory