7 papers · 1 filter
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…
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…
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…