Algebra Seminar talk
2026-06-19, 13:30
Aris Demelius
Suslin Trees and the Suslin Problem
Abstract:
$\mathbb{R}$ is the only complete dense linear order (DLO) that is separable. Is it also the only complete DLO that satisfies the countable chain condition (ccc)? This question is known as the Suslin Problem. A Suslin line is a DLO satisfying the ccc which is not separable. A Suslin tree is a tree of height $\omega_{1}$ with no cofinal branch and satisfying the ccc. We show that there exists a Suslin tree if and only if there exists a Suslin line. Then we show that if $\mathrm{MA}(\aleph_{1})$ holds, there is no Suslin tree.