6 papers
Representing a ring as the endomorphism ring of an abelian group
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
We investigate Baer's realization problem for almost free abelian groups, focusing on the extent to which rings can be represented as endomorphism rings under strong freeness condi…
Failure of singular compactness for Hom
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
Assuming Gödel's axiom of constructibility , we construct a -free abelian group of singular cardinality for some suitable cardinal which is regular and uncountable,…
Quite free p-groups with trivial duality
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
We present a class of abelian groups that exhibit a high degree of freeness while possessing no non-trivial homomorphisms to a canonical free object. Unlike prior investigations, w…
On groups well represented as automorphism groups of groups
Mohsen Asgharzadeh, Mohammad Golshani, Daniel Herden +1
Assuming Gödel's axiom of constructibility we present a characterization of those groups for which there exist arbitrarily large groups such that $aut(H)…
Expressive Power of Infinitary Logic and Absolute co-Hopfianity
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
Recently, Paolini and Shelah have constructed absolutely Hopfian torsion-free abelian groups of any given size. In contrast, we show that this is not necessarily the case for absol…
Naturality and Definability III
Mohsen Asgharzadeh, Mohammad Golshani, Saharon Shelah
In this paper, we deal with the notions of naturality from category theory and definablity from model theory and their interactions. In this regard, we present three results. First…