منابع مشابه
Some ugly א1-free abelian groups
Given an א1-free abelian group G we characterize the class CG of all torsion abelian groups T satisfying Ext(G, T ) = 0 assuming the special continuum hypothesis CH. Moreover, in Gödel’s constructable universe we prove that this characterizes CG for arbitrary torsion-free abelian G. It follows that there exist some ugly א1-free abelian groups.
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Themain purpose of this paper is to prove that if X= {Xa,pab,A} is a usual א1directed inverse system of continuous images of arcs with monotone bonding mappings, then X = limX is a continuous image of an arc (Theorem 2.4). Some applications of this statement are also given.
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It is proved consistent with either CH or ¬CH that there is an א1separable group of cardinality א1 which does not have a coherent system of projections. It had previously been shown that it is consistent with ¬CH that every א1-separable group of cardinality א1 does have a coherent system of projections.
متن کاملThe Kaplansky Test Problems for א1-separable Groups
We answer a long-standing open question by proving in ordinary set theory, ZFC, that the Kaplansky test problems have negative answers for א1-separable abelian groups of cardinality א1. In fact, there is an א1-separable abelian group M such that M is isomorphic to M ⊕M ⊕M but not to M ⊕M . We also derive some relevant information about the endomorphism ring of M .
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ژورنال
عنوان ژورنال: Annals of Mathematical Logic
سال: 1978
ISSN: 0003-4843
DOI: 10.1016/s0003-4843(78)80002-3