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Is it possible to set a collection's permissions to public via either the Node or REST apis?
If so, how so?
You cannot do this on a per collection via node or rest, no.
You can make a business logic script to query the collection and iterate over the returned results, and set them as "gr" (globally readable). You can read more about acl's over here http://devcenter.kinvey.com/rest/guides/security#entityanduserpermissions