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Jeff Burdges
Jeff Burdges
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I think the 'status' might be described as : Pillay has shown using used Selah's work that the free group is not CM-trivial.

All known counterexamples to Zilber's conjecture are CM-trivial. A non-abelian simple group of finite Morley rank is not CM-trivial. We therefore suspect that the current methods based upon the Hrushovski's counterexamples cannot produce even an infinite rank counterexample who is a simple group.

I think the 'status' might be described as : Pillay has shown using used Selah's work that the free group is not CM-trivial.

All known counterexamples to Zilber's conjecture are CM-trivial. A non-abelian simple group of finite Morley rank is not CM-trivial. We therefore suspect that the current methods based upon the Hrushovski's counterexamples cannot produce even an infinite rank counterexample who is a simple group.

I think the 'status' might be described as : Pillay has shown using used Selah's work that the free group is not CM-trivial.

All known counterexamples to Zilber's conjecture are CM-trivial. A non-abelian simple group of finite Morley rank is not CM-trivial. We therefore suspect that the current methods based upon Hrushovski's counterexamples cannot produce even an infinite rank counterexample who is a simple group.

Source Link
Jeff Burdges
Jeff Burdges
  • 565
  • 1
  • 4
  • 9

I think the 'status' might be described as : Pillay has shown using used Selah's work that the free group is not CM-trivial.

All known counterexamples to Zilber's conjecture are CM-trivial. A non-abelian simple group of finite Morley rank is not CM-trivial. We therefore suspect that the current methods based upon the Hrushovski's counterexamples cannot produce even an infinite rank counterexample who is a simple group.