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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