D. Herden

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20192022

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math.GR2022

Forcing a Basis into $ℵ_{1}$ -Free Groups

Daniel Bossaller, Daniel Herden, Alexandra V. Pasi

In this paper, we address the question of when a non-free $ℵ_{1}$ -free group $H$ can be be free in a transitive cardinality-preserving model extension. Using the $Γ$ -invariant,…

math.GR2021

On the absoluteness of $ℵ_{1}$ -freeness

Daniel Herden, Alexandra V. Pasi

$ℵ_{1}$ -free groups, abelian groups for which every countable subgroup is free, exhibit a number of interesting algebraic and set-theoretic properties. In this paper, we give a…

math.GR2019

$ℵ_{k}$ -free cogenerators

Manfred Dugas, Daniel Herden, Saharon Shelah

We prove in ZFC that an abelian group $C$ is cotorsion if and only if $Ext (F, C) = 0$ for every $ℵ_{k}$ -free group $F$ , and discuss some consequences and related r…

Forcing a Basis into ℵ1​-Free Groups

On the absoluteness of ℵ1​-freeness

ℵk​-free cogenerators

Forcing a Basis into $ℵ_{1}$ -Free Groups

On the absoluteness of $ℵ_{1}$ -freeness

$ℵ_{k}$ -free cogenerators