## Logic Seminar

Shihao XiongCornell University
Aronszajn and Kurepa Trees
Tuesday, December 10, 2019 - 2:55pm
Malott 206

Monroe Eskew asked whether the tree property at $\omega_2$ implies there is no Kurepa tree as in the case in the Mitchell model, or under PFA. James Cummings answered this question in the negative in 2016 in his paper Aronszajn and Kurepa Trees, i.e., the tree property at $\omega_2$ is consistent with the existence of $\omega_1$-trees with as many branched as desired. I’ll present James Cummings’ result.