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The Canary Tree

Published online by Cambridge University Press:  20 November 2018

Alan H. Mekler
Affiliation:
Department of Mathematics and Statistics Simon Fraser University Burnaby, British Columbia V5A 1S6
Saharon Shelah
Affiliation:
Institute of Mathematics The Hebrew University Jerusalem 91904, Israel and Department of Mathematics Rutgers University New Brunswick, New Jersey 08903 USA
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Abstract

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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.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1993

References

1. Baumgartner, J., Harrington, L. and Kleinberg, G., Adding a closed unbounded set, J. Symbolic Logic 41(1976), 481482.Google Scholar
2. Hyttinen, T. and Tuuri, H., Constructing strongly equivalent nonisomorphic models for unstable theories, Ann. Pure and Appl. Logic 52(1991), 203248.Google Scholar
3. Hyttinen, T. and J. Vàänänen, On Scott and Karp trees of uncountable models, J. Symbolic Logic 55(1990), 897908.Google Scholar
4. Mekler, A. and J. Vàänänen, Trees and π1 1 -subsets of w1w1 , submitted.Google Scholar
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