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The Canary Tree

Published online by Cambridge University Press:  20 November 2018

Alan H. Mekler  and
Saharon Shelah
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

03E35 (03C75)
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 36 , Issue 2 , 01 June 1993 , pp. 209 - 215
Copyright
Copyright © Canadian Mathematical Society 1993

References

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4. Mekler, A. and J. Vàänänen, Trees and π1 1 -subsets of w1w1 , submitted.Google Scholar