Journal of Symbolic Logic

Aronszajn lines and the club filter

Justin Tatch Moore

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The purpose of this note is to demonstrate that a weak form of club guessing on ω1 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 ω-proper forcings.

Article information

J. Symbolic Logic, Volume 73, Issue 3 (2008), 1029-1035.

First available in Project Euclid: 27 December 2008

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E05: Other combinatorial set theory 03E35: Consistency and independence results

Aronszajn club guessing Countryman forcing axiom ω-proper


Moore, Justin Tatch. Aronszajn lines and the club filter. J. Symbolic Logic 73 (2008), no. 3, 1029--1035. doi:10.2178/jsl/1230396763.

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