Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-19T12:01:05.748Z Has data issue: false hasContentIssue false
  • English
  • Français

Aronszajn lines and the club filter

Published online by Cambridge University Press:  12 March 2014

Justin Tatch Moore
Justin Tatch Moore*
Affiliation:
Department of Mathematics, Cornell University, Ithaca, NY 14853-4201, USA, E-mail: justin@math.cornell.edu
Get access Rights & Permissions [Opens in a new window]

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.

Keywords

Aronszajnclub guessingCountrymanforcing axiomω-proper
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 73 , Issue 3 , September 2008 , pp. 1029 - 1035
Copyright
Copyright © Association for Symbolic Logic 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Jech, Thomas, Set theory, second ed., Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1997.CrossRefGoogle Scholar
[2]Kunen, Kenneth, An introduction to independence proofs, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland, 1983.Google Scholar
[3]Moore, Justin Tatch, Persistent counterexamples to basis conjectures, Circulated note, 09 2004.Google Scholar
[4]Moore, Justin Tatch, Set mapping reflection, Journal of Mathematical Logic, vol. 5 (2005), no. 1, pp. 87–97.CrossRefGoogle Scholar
[5]Moore, Justin Tatch, A five element basis for the uncountable linear orders, Annals of Mathematics (2), vol. 163 (2006), no. 2, pp. 669–688.CrossRefGoogle Scholar
[6]Moore, Justin Tatch, A solution to the L space problem, Journal of the American Mathematical Society, vol. 19 (2006), no. 3, pp. 717–736.CrossRefGoogle Scholar
[7]Shelah, Saharon, Decomposing uncountable squares to countably many chains, Journal of Combinatorial Theory Series A, vol. 21 (1976), no. 1, pp. 110–114.CrossRefGoogle Scholar
[8]Todorcevic, Stevo, Partitioning pairs of countable ordinals, Acta Mathematica, vol. 159 (1987), no. 3–4, pp. 261–294.CrossRefGoogle Scholar
[9]Todorcevic, Stevo, Lipschitz maps on trees, Journal of the Institute of Mathematics of Jussieu. Journal de l'Institut de Mathématiques de Jussieu, vol. 6 (2007), no. 3, pp. 527–556.CrossRefGoogle Scholar
[10]Todorcevic, Stevo, Walks on ordinals and their characteristics, Progress in Mathematics, vol. 263, Birkhäuser, 2007.CrossRefGoogle Scholar