Journal of Symbolic Logic

Aronszajn lines and the club filter

Justin Tatch Moore

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Abstract

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

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

Dates
First available in Project Euclid: 27 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1230396763

Digital Object Identifier
doi:10.2178/jsl/1230396763

Mathematical Reviews number (MathSciNet)
MR2444284

Zentralblatt MATH identifier
1165.03030

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

Keywords
Aronszajn club guessing Countryman forcing axiom ω-proper

Citation

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


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