5 papers
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 uncountab…
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…
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…
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…
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…