The canary tree
by Mekler and Shelah. [MkSh:398]
Canadian J Math Journal Canadien de Mathematiques, 1993
A canary tree is a tree of cardinality the continuum which
has no uncountable branch, but gains a branch whenever a stationary
set is destroyed (without adding reals). Canary trees are important
in infinitary model theory. The existence of a canary tree is
independent of ZFC + GCH.
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