Some consequences of MA + ¬wKH

Abstract Let wKH denote the following statement: There exists a ω 1 -tree of power ω 1 with >ω 1 ω 1 -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 ω 1 ; (b) Every LOTS of density ω 1 has a θ-disjoint π-base; (c) There is no Baire LOTS of power ω 1 without isolated points; (d) Every perfectly normal non-Archimedian space of weight ω 1 is metrizable. These results are connected to problems from [4], [10], [7] and [15], respectively. A part of these results was announced in [17].