Is Entscheidungsproblem in Co-RE? And Proof if it is. As I study through, I learned that Entscheidungsproblem has a negative answer. Then I came to wonder whether the problem is in Co-RE. If it is, can anyone show me the proof? Thanks.

From wikipedia

> The Entscheidungsproblem has often been identified in particular with the decision problem for first-order logic (that is, the problem of algorithmically determining whether a first-order statement is universally valid).

The set of universally valid first-order statements is known to be r.e. and not recursive. If it was co-r.e. (by which I mean its complement is r.e.), then it would be recursive. (A set that is both r.e. and co-r.e. is recursive). Hence it is not co-r.e.