Abstract
We show that in the language of {≤}, the Π₃-fragment of the first order theory of the Σ⁰₂-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 Δ⁰₂-degrees is undecidable.
Citation
Thomas F. Kent. "The Π₃-theory of the Σ⁰₂-enumeration degrees is undecidable." J. Symbolic Logic 71 (4) 1284 - 1302, December 2006. https://doi.org/10.2178/jsl/1164060455
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