The special Aronszajn tree property at ℵ₂ and GCH

2018/09/20 by Asperó, David, Golshani, Mohammad
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1809.07638

Abstract

Starting from the existence of a weakly compact cardinal, we build a generic extension of the universe in which GCH holds and all ℵ₂-Aronszajn trees are special and hence there are no ℵ₂-Souslin trees. This result answers a well-known open question from the 1970's.

Related

• The Special Aronszajn Tree Property
• The Special Aronszajn Tree Property at κ⁺ and \square_{κ, 2}
• The Special Tree Number
• The Tree Property up to ℵ_ω²
• How special is your Aronszajn tree?