Destructibility of the tree property at $\aleph_{\omega+1}$
Yair Hayut, Menachem Magidor
TL;DR
This paper constructs a model where the tree property at le _{\u00f4mega+1} is initially present but can be destroyed by certain forcings, and discusses conditions for its indestructibility.
Contribution
It demonstrates the destructibility of the tree property at le _{\u00f4mega+1} and explores cases of its indestructibility under specific forcings.
Findings
Tree property can be destroyed by ol(ll( ,ll_1)).
Conditions for indestructibility under small or closed forcings.
Constructed a model with the property at le _{\u00f4mega+1}.
Abstract
We construct a model in which the tree property holds in and it is destructible under . On the other hand we discuss some cases in which the tree property is indestructible under small or closed forcings.
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Taxonomy
TopicsComputability, Logic, AI Algorithms · Advanced Topology and Set Theory · Economic theories and models