2 problems

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Non-universality conjecture for height-one locally countable Borel quasi-orders
A quasi-order $(P,\leq_P)$ is a reflexive and transitive relation, and its height is the length of the longest strictly decreasing chain, equivalently the height of the partial ord…
Conjectureopencomputability-theory descriptive-set-theory quasi-ordersarXiv posted 2 days ago
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The $f(3)=3$ conjecture for dominating sets in three quasi-orders
For every positive integer $k$ , let $f(k)$ be an integer such that every complete multidigraph whose arcs are the union of $k$ quasi-orders has a dominating set of size at most…
Conjectureopendominating-sets geometric-hypergraphs quasi-ordersarXiv posted 2 days ago

Non-universality conjecture for height-one locally countable Borel quasi-orders