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On our paper `Almost Free Splitter', a correction

Rüdiger Göbel·Saharon Shelah
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Abstract

Let R be a subring of Q and recall from math.LO/9910161 that an R-module 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 non-free aleph_1-free splitter of cardinality aleph_1.

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Rüdiger Göbel, Saharon Shelah. 2000-09-06. On our paper `Almost Free Splitter', a correction. https://arxiv.org/abs/math/0009063

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