27 citations · 87 across the 9 of their papers we have counts for
9 papers
The power of trees
Ari Meir Brodsky, Assaf Rinot, Shira Yadai
We give two consistent constructions of trees whose finite power is sharply different from : 1. An -tree whose interval topology is perfectly…
Proxy principles in combinatorial set theory
Ari Meir Brodsky, Assaf Rinot, Shira Yadai
The parameterized proxy principles were introduced by Brodsky and Rinot in a 2017 paper, as new foundations for the construction of -Souslin trees in a uniform way that does not…
A microscopic approach to Souslin-tree construction, Part II
Ari Meir Brodsky, Assaf Rinot
In Part I of this series, we presented the microscopic approach to Souslin-tree constructions, and argued that all known -based constructions of Souslin trees with va…
Density of uniqueness triples from the diamond axiom
Ari Meir Brodsky, Adi Jarden
We work with a pre--frame, which is an abstract elementary class (AEC) endowed with a collection of basic types and a non-forking relation satisfying certain natural properties…
Distributive Aronszajn trees
Ari Meir Brodsky, Assaf Rinot
Ben-David and Shelah proved that if is a singular strong-limit cardinal and , then entails the existence of a normal -distributive -Aronszajn tre…
More notions of forcing add a Souslin tree
Ari Meir Brodsky, Assaf Rinot
An -Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech…
A Microscopic approach to Souslin-tree constructions. Part I
Ari Meir Brodsky, Assaf Rinot
We propose a parameterized proxy principle from which -Souslin trees with various additional features can be constructed, regardless of the identity of . We then introduce th…
Reduced powers of Souslin trees
Ari Meir Brodsky, Assaf Rinot
We study the relationship between a -Souslin tree and its reduced powers . Previous works addressed this problem from the viewpoint of a single power , wh…
A Theory of Stationary Trees and the Balanced Baumgartner-Hajnal-Todorcevic Theorem for Trees
Ari Meir Brodsky
Building on early work by Stevo Todorcevic, we describe a theory of stationary subtrees of trees of successor-cardinal height. We define the diagonal union of subsets of a tree, as…