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Finding paths through narrow and wide trees

Published online by Cambridge University Press:  12 March 2014

Stephen Binns  and
Bjørn Kjos-Hanssen
Stephen Binns
Affiliation:
Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia, E-mail: [email protected]
Bjørn Kjos-Hanssen
Affiliation:
Department of Mathematics, University of Hawai‘i at Mānoa, Honolulu, Hi 96822, USA, E-mail: [email protected]
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Abstract

We consider two axioms of second-order arithmetic. These axioms assert, in two different ways, that infinite but narrow binary trees always have infinite paths. We show that both axioms are strictly weaker than Weak König's Lemma, and incomparable in strength to the dual statement (WWKL) that wide binary trees have paths.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 74 , Issue 1 , March 2009 , pp. 349 - 360
Copyright
Copyright © Association for Symbolic Logic 2009

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References

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