Extending partial isometries

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On subgroups of minimal topological groups (2000, unknown): “tric and M∗ = L. I am indebted to the referee for catching this error. 2. The referee raised the question whether the methods of this section could be used to prove the following result by S. Solecki [40] and A.M. Vershik [56] that extends an earlier result by Hrushovski: for every ﬁnite metric spac”
Turbulence, amalgamation, and generic automorphisms of homogeneous structures (2004, background): “th the JEP for Kn p, which is usually not hard to verify, implies the existence of ample generics. For example, this easily works for the class of ﬁnite graphs. Another case is the following. Solecki [45] and, independently, Vershik have shown that the class K of ﬁnite metric spaces with rational di”
Structural Ramsey theory of metric spaces and topological dynamics of isometry groups (2008, unknown): “Gon Gnis the action deﬁned by: g·(h1,...,hn) = (gh1g−1,...,ghng−1). An element (h1,...,hn) of Gn is cyclically dense if for some g∈G, the set {gk·(h1,...,hn) : k∈ω}is dense in Gn. Theorem 90 (Solecki [88]). All the diagonal actions of iso(U) have cyclically dense elements. Theorem 91 (Solecki [88]).”
A topological version of the Bergman property (2005, background): “Namely, one should think of the Bergman property as a strong generalisation of finiteness and of property (OB) as a strong generalisation of compactness.”