arXiv subjects

John Susice

Publications and source records attributed to John Susice.

2 recordsLinked to original sources

arXiv2019

Chang's Conjecture with $\square_{ω_1, 2}$ from an $ω_1$-Erdős Cardinal

Answering a question of Sakai, we show that the existence of an $ω_1$-Erdős cardinal suffices to obtain the consistency of Chang's Conjecture with $\square_{ω_1, 2}$. By a result of Donder this is best possible. We also give an answer to another question of Sakai relating to the incompatibility of $\square_{λ, 2}$ and $(λ^+, λ) \twoheadrightarrow (κ^+, κ)$ for uncountable $κ$.

math.LO↗

arXiv2019

The Special Aronszajn Tree Property at $κ^+$ and $\square_{κ, 2}$

We show that for any regular cardinal $κ$, $\square_{κ, 2}$ is consistent with "all $κ^+$-Aronszajn trees are special." By a result of Shelah and Stanley this is optimal in the sense that $\square_{κ, 2}$ may not be strengthened to $\square_κ$. Using methods of Golshani and Hayut we obtain our consistency result simultaneously for all regular $κ$.

math.LO↗