7 papers · 1 filter
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 Fraïss…
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…
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…
The Slicing Axioms
Ziemowit Kostana, Saharon Shelah
We introduce the family of axioms, denoted , that claim the existence of strictly increasing decompositions of the form w…
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…
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…
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…