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Summer 2002 On problems by Baer and Kulikov using $V=L$
Lutz Strüngmann
Illinois J. Math. 46(2): 477-490 (Summer 2002). DOI: 10.1215/ijm/1258136204

Abstract

Let $T$ be a torsion abelian group and $\lambda$ a cardinal. Among all torsion-free abelian groups $H$ of rank less than or equal to $\lambda$ satisfying $\operatorname{Ext}(H,T)=0$ a group $G$ is called $\lambda$-universal for $T$ if it is universal with respect to group-embedding. We show that in Gödel's constructible universe ($V=L$) there always exists a $\lambda$-universal group for $T$ if $T$ has only finitely many non-trivial bounded $p$-components. This answers a question by Kulikov in the affirmative. Moreover, we prove that in $V=L$ for a large class of torsion-free abelian groups $G$ there exists a completely decomposable group $C$ such that $\operatorname{Ext}(G,T^{\prime})=0$ if and only if $\operatorname{Ext}(C,T^{\prime})=0$ for any torsion abelian group $T^{\prime}$. This is related to a question of Baer.

Citation

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Lutz Strüngmann. "On problems by Baer and Kulikov using $V=L$." Illinois J. Math. 46 (2) 477 - 490, Summer 2002. https://doi.org/10.1215/ijm/1258136204

Information

Published: Summer 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1013.20053
MathSciNet: MR1936930
Digital Object Identifier: 10.1215/ijm/1258136204

Subjects:
Primary: 20K20
Secondary: 20K15, 20K40

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 2 • Summer 2002
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