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Aug 30, 2020 at 8:38 comment added Stefaan Vaes I think that in your question, your are only mentioning countability of equivalence classes. Maybe you can post a new and more precise question about these other points that you have in mind.
Aug 29, 2020 at 6:05 comment added Chilperic Thanks very much, Stefaan and YCor. I was aware of some of this work on cardinality of these classes. I was wondering more about thinking of them along the results we have for countable Borel equivalence relations. Does Silver's dichotomy hold -- either countable number of classes or an uncountable number of singletons? Is it possible to have a group action so that the classes are orbits? That sort of thing.
Aug 28, 2020 at 12:47 history answered Stefaan Vaes CC BY-SA 4.0