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THE TREE PROPERTY AT THE TWO IMMEDIATE SUCCESSORS OF A SINGULAR CARDINAL
Part of:
Set theory
Published online by Cambridge University Press: 10 July 2020
Abstract
We present an alternative proof that from large cardinals, we can force the tree property at
$\kappa ^+$
and
$\kappa ^{++}$
simultaneously for a singular strong limit cardinal
$\kappa $
. The advantage of our method is that the proof of the tree property at the double successor is simpler than in the existing literature. This new approach also works to establish the result for
$\kappa =\aleph _{\omega ^2}$
.
MSC classification
Secondary:
03E55: Large cardinals
- Type
- Article
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- Copyright
- © The Association for Symbolic Logic 2020
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