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ON THE HISTORY TREE
Keywords:
tree in set theory, ideal in partial order.DOI:
https://doi.org/10.17654/0974165822040Abstract
A tree in set theory is a partial order $\left(T, \leq_T\right)$ such that the set of predecessors of each element $t \in T$ is well-ordered. We introduce the notion of history tree and give a sufficient condition for the existence of an isomorphism between a tree and its history tree.
Received: August 2, 2022
Accepted: September 10, 2022
References
Thomas Jech, Set Theory, Springer-Verlag, Berlin Heidelberg, 2003.
Kenneth Kunen, Set theory, An Introduction to Independence Proofs, Studies in Logic and the Foundations of Mathematics, Amsterdam, New York, Oxford, Vol. 102, 1980.
Assaf Rinot, Antichains in partially ordered sets of singular confinality, Arch. Math. Logic 46(5-6) (2007), 457-464.
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