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Archive for Mathematical Logic

, Volume 57, Issue 1–2, pp 83–90 | Cite as

Aronszajn and Kurepa trees

  • James CummingsEmail author
Article
  • 57 Downloads

Abstract

Monroe Eskew (Tree properties on \(\omega _1\) and \(\omega _2\), 2016. https://mathoverflow.net/questions/217951/tree-properties-on-omega-1-and-omega-2) asked whether the tree property at \(\omega _2\) implies there is no Kurepa tree (as is the case in the Mitchell model, or under PFA). We prove that the tree property at \(\omega _2\) is consistent with the existence of \(\omega _1\)-trees with as many branches as desired.

Keywords

Aronszajn tree Kurepa tree Mitchell forcing Forcing axioms 

Mathematics Subject Classification

03E35 

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References

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

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