Full Souslin trees at small cardinals
Assaf Rinot, Shira Yadai, Zhixing You

TL;DR
This paper demonstrates the consistent existence of full - ext{Souslin} trees at small cardinals, specifically _2, with properties that their countable products remain _2- ext{Souslin} trees, addressing a question by Kunen.
Contribution
It proves the consistent existence of full - ext{Souslin} trees at _2, with a large family whose products preserve the _2- ext{Souslin} property, at small cardinals.
Findings
Existence of _2- ext{full} _2- ext{Souslin} trees is consistent.
There can be _3 many such trees with product properties.
The product of countably many such trees remains _2- ext{Souslin}.
Abstract
A -tree is said to be full if each of its limit levels omits no more than one potential branch. Kunen asked whether a full -Souslin tree may consistently exist. Shelah gave an affirmative answer of height a strong limit Mahlo cardinal. Here, it is shown that these trees may consistently exist at small cardinals. Indeed, there can be many full -trees such that the product of any countably many of them is an -Souslin tree.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Computability, Logic, AI Algorithms · Rings, Modules, and Algebras
