Aronszajn lines and the club filter

The purpose of this note is to demonstrate that a weak form of club guessing on 1 implies the existence of an Aronszajn line with no Countryman suborders. An immediate consequence is that the existence of a five element basis for the uncountable linear orders does not follow from the forcing axiom for -proper forcings.

• Type: Journal
• Year: 2008
• Where: JSYML
• Authors: Justin Tatch Moore
• Keywords: Countryman Suborders, Immediate Consequence, JSYML 2008, Weak Form