3 problems

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The conjecture that two-graphs do not have ample generics
Two-graphs' non-ample-generics conjecture. Two-graphs do not have ample generics.
Conjectureopenample-generics partial-automorphisms two-graphsarXiv posted 2 days ago
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Truss's conjecture on ample generics for the automorphism group of the rational homogeneous poset
Let $\mathcal D$ be the countable homogeneous partially ordered set under discussion, and let $\operatorname{Aut}(\mathcal D)$ denote its automorphism group. A Polish group has amp…
Conjectureopenample-generics homogeneous-structures permutation-groupsarXiv posted 2 days ago
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Non-hyperfinite full groups do not have ample generics
Non-hyperfinite full-group conjecture. If $\mathcal R$ is not hyperfinite, then $[\mathcal R]$ does not have ample generics.
Conjectureopenample-generics equivalence-relations polish-groupsarXiv posted 2 days ago

The conjecture that two-graphs do not have ample generics