From the 1 of 6 linked papers with an AI index.
6 papers
Pure-homogeneous Abelian groups
Ziemowit Kostana
The paper investigates Fraïssé classes of Abelian groups under pure embeddings and characterizes the groups that are universal and homogeneous for several classes, including finite…
Homogeneity of the Lévy collapse from the perspective of Fraïssé theory
Ziemowit Kostana
Given a strongly inaccessible cardinal , we study the Fraïssé class of all Boolean algebras of size , together with regular embeddings. We prove that this is indeed a Fr…
Infinite random graphs
Ziemowit Kostana, JarosÅaw Swaczyna, Agnieszka Widz
We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, w…
Guessing genericity -- looking at parametrized diamonds from a different perspective
Ziemowit Kostana
We introduce and study a family of axioms that closely follows the pattern of parametrized diamonds, studied by Moore, Hrušák, and Džamonja in [13]. However, our approach appeal…
Cohen-like first order structures
Ziemowit Kostana
We study uncountable structures similar to the Fraïssé limits. The standard inductive arguments from the Fraïssé theory are replaced by forcing, so the structures we obtain are…
Discrete subgroups of normed spaces are free
Tomasz Kania, Ziemowit Kostana
Ancel, Dobrowolski, and Grabowski (Studia Math., 1994) proved that every countable discrete subgroup of the additive group of a normed space is free Abelian, hence isomorphic to th…