Some consequences of MA + ¬wKH

Let wKH denote the following statement: There exists a ω₁-tree of power ω₁ with >ω₁ ω₁-branches. First, using methods of 6] and 13], we shall prove theconsistency of MA + ¬wKH. Then we shall prove that MA + ¬wKH implies the following: (a) There is no θ-dense (splitting) poset of power ω₁; (b) Every LOTS of density ω₁ has a θ-disjoint π-base; (c) There is no Baire LOTS of power ω₁ without isolated points; (d) Every perfectly normal non-Archimedian space of weight ω₁ is metrizable. These results are connected to problems from 4], 10], 7] and 15], respectively. A part of these results was announced in 17].