324 citations · 1.7k across the 753 of their papers we have counts for
19 papers · 2 filters
Torsion-free abelian groups are faithfully Borel complete and pure embeddability is a complete analytic quasi-order
Gianluca Paolini, Saharon Shelah
In [9] we proved that the space of countable torsion-free abelian groups is Borel complete. In this paper we show that our construction from [9] satisfies several additional proper…
Adding highly undefinable sets over
Mohammad Golshani, Saharon Shelah
We sow that there exists a generic extension of the Gödel's constructible universe in which diamond holds and there exists a subset such that for stationary many…
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…
When does -categoricity imply -stability?
John T. Baldwin, M. C. Laskowski, Saharon Shelah
For an -categorical atomic class, we clarify the space of types over the unique model of size . Using these results, we prove that if such a class has a model o…
Tiltan and superclub
Shimon Garti, Saharon Shelah
We force superclub with an arbitrary large value of cov(). We force tiltan with an arbitrary large value of add(). Finally, we obtain a negative square br…