The differences between Kurepa trees and Jech-Kunen trees |
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Authors: | Renling Jin |
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Institution: | (1) Department of Mathematics, University of California, 94720 Berkeley, CA, USA |
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Abstract: | Summary By an 1 we mean a tree of power 1 and height 1. An 1-tree is called a Kurepa tree if all its levels are countable and it has more than 1 branches. An 1-tree is called a Jech-Kunen tree if it has branches for some strictly between 1 and
. In Sect. 1, we construct a model ofCH plus
, in which there exists a Kurepa tree with not Jech-Kunen subtrees and there exists a Jech-Kunen tree with no Kurepa subtrees. This improves two results in Ji1] by not only eliminating the large cardinal assumption for Ji1, Theorem 2] but also handling two consistency proofs of Ji1, Theorem 2 and Theorem 3] simultaneously. In Sect. 2, we first prove a lemma saying that anAxiom A focing of size 1 over Silver's model will not produce a Kurepa tree in the extension, and then we apply this lemma to prove that, in the model constructed for Theorem 2 in Ji1], there exists a Jech-Kunen tree and there are no Kurepa trees. |
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Keywords: | 03E35 |
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