Aronszajn trees, square principles, and stationary reflection

2016/05/18 by Lambie-Hanson, Chris
#03E05 #03E35 #03E55 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1605.05489

Abstract

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

Related

• The Special Aronszajn Tree Property at κ⁺ and \square_{κ, 2}
• Club Stationary Reflection and the Special Aronszajn Tree Property
• The special Aronszajn tree property at ℵ₂ and GCH
• Square compactness and Lindelöf trees
• Trees and stationary reflection at double successors of regular cardinals