Aronszajn trees, square principles, and stationary reflection

作者：Lambie Hanson Chris^*

来源：Mathematical Logic Quarterly, 2017, 63(3-4): 265-281.

DOI：10.1002/malq.201600040

We investigate questions involving Aronszajn trees, square principles, and stationary reflection. We first consider two strengthenings of square(kappa) introduced by Brodsky and Rinot for the purpose of constructing kappa-Souslin trees. Answering a question of Rinot, we prove that the weaker of these strengthenings is compatible with stationary reflection at kappa but the stronger is not. We then prove that, if mu is a singular cardinal, square(mu) implies the existence of a special mu(+)-tree with a cf(mu)-ascent path, thus answering a question of Lucke.

• 出版日期2017-11