Shira Yadai

activity

20232025

collaborators

4 papers

math.LO2025

The power of trees

Ari Meir Brodsky, Assaf Rinot, Shira Yadai

We give two consistent constructions of trees $T$ whose finite power $T^{n + 1}$ is sharply different from $T^{n}$ : 1. An $ℵ_{1}$ -tree $T$ whose interval topology $X_{T}$ is perfectly…

math.LO2024

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 $κ$ -Souslin trees in a uniform way that does not…

math.LO2023

The vanishing levels of a tree

Assaf Rinot, Shira Yadai, Zhixing You

We initiate the study of the spectrum $V s p ec (κ)$ of sets that can be realized as the vanishing levels $V (T)$ of a normal $κ$ -tree $T$ . The latter is an invariant in the sense that…

math.LO2023

Full Souslin trees at small cardinals

Assaf Rinot, Shira Yadai, Zhixing You

A $κ$ -tree is said to be full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full $κ$ -Souslin tree may consistently exist. Shelah gave a…