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arXiv · 2206.14177

The invariant random order extension property is equivalent to amenability

Andrei Alpeev
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Abstract

Recently, Glasner, Lin and Meyerovitch gave a first example of a partial invariant order on a certain group that cannot be invariantly extended to an invariant random total order. Using their result as a starting point we prove that any invariant random partial order on a countable group could be invariantly extended to an invariant random total order iff the group is amenable.

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Andrei Alpeev. 2022-06-28. The invariant random order extension property is equivalent to amenability. https://arxiv.org/abs/2206.14177

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