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A RIGID KUREPA TREE FROM A FREE SUSLIN TREE

Part of: Set theory

Published online by Cambridge University Press:  30 January 2025

JOHN KRUEGER
JOHN KRUEGER*
Affiliation:
DEPARTMENT OF MATHEMATICS UNIVERSITY OF NORTH TEXAS 1155 UNION CIRCLE #311430, DENTON TX 76203, USA
*
E-mail: jkrueger@unt.edu
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Abstract

We analyze a countable support product of a free Suslin tree which turns it into a highly rigid Kurepa tree with no Aronszajn subtree. In the process, we introduce a new rigidity property for trees, which says roughly speaking that any non-trivial strictly increasing function from a section of the tree into itself maps into a cofinal branch.

Keywords

free Suslin treeKurepa treerigid tree

MSC classification

Primary: 03E05: Other combinatorial set theory
Secondary: 03E40: Other aspects of forcing and Boolean-valued models
Type
Article
Information
The Journal of Symbolic Logic , First View , pp. 1 - 8
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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References

REFERENCES

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