Authors: Todorčević, Stevo 
Title: Some consequences of MA + ¬wKH
Journal: Topology and its Applications
Volume: 12
Issue: 2
First page: 187
Last page: 202
Issue Date: 1-Jan-1981
ISSN: 0166-8641
DOI: 10.1016/0166-8641(81)90020-1
Abstract: 
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].
Publisher: Elsevier

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