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The Borel Ramsey properties for countable Borel equivalence relations
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We define some natural notions of strong and weak Borel Ramsey properties for countable Borel equivalence relations and show that they hold for a countable Borel equivalence relation if and only if the equivalence relation is smooth. We also consider some variation of the notion for hyperfinite non-smooth Borel equivalence relations.
American Mathematical Society (AMS)
Title: The Borel Ramsey properties for countable Borel equivalence relations
Description:
We define some natural notions of strong and weak Borel Ramsey properties for countable Borel equivalence relations and show that they hold for a countable Borel equivalence relation if and only if the equivalence relation is smooth.
We also consider some variation of the notion for hyperfinite non-smooth Borel equivalence relations.
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