Archive for Mathematical Logic

, Volume 52, Issue 5–6, pp 483–496 | Cite as

Aronszajn trees and the successors of a singular cardinal

Article

Abstract

From large cardinals we obtain the consistency of the existence of a singular cardinal κ of cofinality ω at which the Singular Cardinals Hypothesis fails, there is a bad scale at κ and κ++ has the tree property. In particular this model has no special κ+-trees.

Keywords

Large cardinals Forcing Tree property Special tree Bad scale 

Mathematics Subject Classification (2000)

03E35 03E55 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

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