The Π3-theory of the -enumeration degrees is undecidable
Thomas F. Kent · Journal of Symbolic Logic · 2006
Abstract We show that in the language of { ≤ }. the Π3-fragment of the first order theory of the -enumeration degrees is undecidable. We then extend this result to show that the Π3-theory of any substructure of the enumeration degrees which contains the -degrees is undecidable.