Ziemowit Kostana

activity

20182026

collaborators

11 papers

math.GR2026

Pure-homogeneous Abelian groups

Ziemowit Kostana

We study Fraïssé classes of Abelian groups with pure embeddings. We characterize Abelian groups that are universal and homogeneous for: finitely co-generated groups, finite groups,…

math.LO2026

Homogeneity of the Lévy collapse from the perspective of Fraïssé theory

Ziemowit Kostana

Given a strongly inaccessible cardinal $λ$ , we study the Fraïssé class of all Boolean algebras of size $< λ$ , together with regular embeddings. We prove that this is indeed a Fraïss…

math.CO2026

Infinite random graphs

Ziemowit Kostana, Jarosław 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…

math.FA2024

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…

math.LO2024

Diamond on Kurepa trees

Ziemowit Kostana, Assaf Rinot, Saharon Shelah

We introduce a new weak variation of diamond that is meant to only guess the branches of a Kurepa tree. We demonstrate that this variation is considerably weaker than diamond by pr…

math.LO2023

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 appeals t…

math.LO2021

The Slicing Axioms

Ziemowit Kostana, Saharon Shelah

We introduce the family of axioms, denoted $Slice_{κ}$ , that claim the existence of strictly increasing decompositions of the form $2^{δ} = α < κ ⋃ 2^{δ} \cap M_{α},$ w…

math.LO2021

What would the rational Urysohn space and the random graph look like if they were uncountable?

Ziemowit Kostana

Building on the work of Avraham, Rubin, and Shelah, we aim to build a variant of the Fraïssé theory for uncountable models built from finite submodels. With this aim, we generalize…

math.LO2020

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 hig…

math.LO2019

On countably saturated linear orders and certain class of countably saturated graphs

Ziemowit Kostana

The idea of this paper is to explore the existence of canonical countably saturated models for different classes of structures. It is well-known that, under CH, there exists a uniq…

math.GN2018

Non-meagre subgroups of reals disjoint with meagre sets

Ziemowit Kostana

Let $(X, +)$ denote $(R, +)$ or $(2^{ω}, +_{2})$ . We prove that for any meagre set $F \subseteq X$ there exists a subgroup $G \leq X$ without the Baire property, disjoint with…