10 papers
Forcing axioms and the structure theory of Aronszajn trees
Justin Tatch Moore, Stevo Todorcevic
We study which structural results about Aronszajn trees require the Proper Forcing Axiom and which require only MA(aleph1). In particular, we show that MA(aleph1) is consistent wit…
Strong colorings based on oscillations
Stevo Todorcevic, Jing Zhang
We show that for any uncountable cardinal , there is a coloring such that for any of order type that are stationary…
Square-bracket operations clubs
Osvaldo Guzman, Stevo Todorcevic
This paper continues the investigation of the three square-bracket operations from chapter 5 of \cite{Walks}. \ We say that a square-bracket operation …
Forcing Axioms and construction schemes
Jorge Antonio Cruz Chapital, Osvaldo Guzman, Stevo Todorcevic
We continue the development of the theory of construction schemes over as introduced by the third author by studying their relation with forcing axioms. Formally, we introduc…
On Big Ramsey degrees of universal -edge-labeled hypergraphs
Jan Hubička, Matěj Konečný, Stevo Todorcevic +1
We show that the big Ramsey degrees of every countable universal -uniform -edge-labeled hypergraph are infinite for every . Together with a recent result of Braunfel…
Posets of Copies of Countable Ultrahomogeneous Tournaments
Miloš S. Kurilić, Stevo Todorčević
The poset of copies of a relational structure is the partial order ${\mathbb P} ({\mathbb X} ) := \langle \{ Y \subset X: {\mathbb Y} \cong {\mathbb X}\}, \subset \ra…
Higher Dimensional Chain Conditions
Stevo Todorcevic, Jing Zhang
We investigate higher dimensional chain conditions, where the largeness notion is given by Fubini products of a given ideal. From strong saturation properties of an ideal, we deriv…
Infinite dimensional sequential compactness: Sequential compactness based on barriers
Cesar Corral, Osvaldo Guzman, Carlos Lopez-Callejas +3
We introduce a generalization of sequential compactness using barriers on extending naturally the notion introduced in [W. Kubiś and P. Szeptycki, On a topological Ramsey theor…
Can You Take Komjath's Inaccessible Away?
Hossein Lamei Ramandi, Stevo Todorcevic
In this paper we aim to compare Kurepa trees and Aronszajn trees. Moreover, we analyze the affect of large cardinal assumptions on this comparison. Using the the method of walks on…
Pre-compact families of finite sets of integers and weakly null sequences in Banach spaces
Jordi Lopez Abad, S. Todorcevic
Two applications of Nash-Williams' theory of barriers to sequences on Banach spaces are presented: The first one is the -saturation of , countable compacta. The seco…