The canary tree

Preprint English OPEN
Mekler, Alan H. ; Shelah, Saharon (1993)
  • Subject: Mathematics - Logic

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.
  • References (4)

    [1] Baumgartner, J., Harrington, L. and Kleinberg, G. Adding a closed unbounded set, J. Symbolic Logic 41(1976) 481-482.

    [2] Hyttinen, T. and Tuuri, H. Constructing strongly equivalent nonisomorphic models for unstable theories, Ann. Pure and Appl. Logic 52(1991) 203-248.

    [3] Hyttinen, T and V¨a¨an¨anen, J. On Scott and Karp trees of uncountable models, J. Symbolic Logic 55(1990) 897-908.

    [4] Mekler, A. and V¨a¨an¨anen, J., Trees and Π11-subsets of ω1ω1, submitted.

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