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## A characterization of $\mathop{\rm Ext}(G,\mathbb Z)$ assuming $(V=L)$

### Tom 193 / 2007

Fundamenta Mathematicae 193 (2007), 141-151 MSC: Primary 20K15, 20K20, 20K35, 20K40; Secondary 18E99, 20J05. DOI: 10.4064/fm193-2-3

#### Streszczenie

We complete the characterization of $\mathop{\rm Ext}(G,\mathbb Z)$ for any torsion-free abelian group $G$ assuming Gödel's axiom of constructibility plus there is no weakly compact cardinal. In particular, we prove in $(V=L)$ that, for a singular cardinal $\nu$ of uncountable cofinality which is less than the first weakly compact cardinal and for every sequence $( \nu_p : p \in \varPi )$ of cardinals satisfying $\nu_p \leq 2^{\nu}$ (where $\varPi$ is the set of all primes), there is a torsion-free abelian group $G$ of size $\nu$ such that $\nu_p$ equals the $p$-rank of $\mathop{\rm Ext}(G,\mathbb Z)$ for every prime $p$ and $2^{\nu}$ is the torsion-free rank of $\mathop{\rm Ext}(G,\mathbb Z)$.

#### Autorzy

• Saharon ShelahDepartment of Mathematics
The Hebrew University of Jerusalem
Jerusalem 91904, Israel
and}
Rutgers University
New Brunswick, NJ 08903, U.S.A.
e-mail
• Lutz StrüngmannDepartment of Mathematics
University of Duisburg-Essen
45117 Essen, Germany
and
Department of Mathematics
University of Hawaii
2565 McCarthy Mall
Honolulu, HI 96822-2273, U.S.A.
e-mail

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