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Jul 1, 2015 at 17:31 comment added user75594 Thank you for counterexample professor Pillay. I have read the above statement many years ago and do not remember where. So, apparently, I missed some important condition of context. Maybe $K$ must be finitely generated and finite transcendence degree over the constants.
May 22, 2015 at 20:07 history answered Anand Pillay CC BY-SA 3.0