On our paper `Almost Free Splitter', a correction
Abstract
Let R be a subring of Q and recall from math.LO/9910161 that an Rmodule G is a splitter if Ext_R(G,G)=0. We correct the statement of Main Theorem 1.5 in math.LO/9910161. Assuming CH any aleph_1$free splitter of cardinality aleph_1 is free over its nucleus as shown in math.LO/9910161. Generally these modules are very close to being free as explained below. This change follows from math.LO/9910161 and is due to an incomplete proof (noticed thanks to Paul Eklof) in the first section of math.LO/9910161. Assuming the negation of CH, in Shelah [Sh:F417] (work in progress) it will be shown that under Martin's axiom these splitters are free indeed. However there are models of set theory having nonfree aleph_1free splitter of cardinality aleph_1.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 September 2000
 DOI:
 10.48550/arXiv.math/0009063
 arXiv:
 arXiv:math/0009063
 Bibcode:
 2000math......9063G
 Keywords:

 Logic;
 Rings and Algebras