P-ideal dichotomy and a strong form of the Suslin Hypothesis
Volume 251 / 2020
Fundamenta Mathematicae 251 (2020), 17-33 MSC: Primary 03E35; Secondary 03E05. DOI: 10.4064/fm864-2-2020 Published online: 19 June 2020
We introduce a forcing notion which forces the P-ideal dichotomy, while every almost Suslin tree from the ground model remains non-special. Thus, while the P-ideal dichotomy implies the Suslin Hypothesis, or equivalently that every Aronszajn tree has an uncountable antichain, it does not imply that every Aronszajn tree has a stationary antichain.