- Scranton, United States
Thomas Kent
Marywood University, Mathematics, Faculty Member
Research Interests:
Research Interests: Computer Science and AMIA
We show that the first order theory of the Σ02 s-degrees is undecid-able. Via isomorphism of the s-degrees with the Q-degrees, this also shows that the first order theory of the Π02 Q-degrees is undecidable. Together with a result of... more
We show that the first order theory of the Σ02 s-degrees is undecid-able. Via isomorphism of the s-degrees with the Q-degrees, this also shows that the first order theory of the Π02 Q-degrees is undecidable. Together with a result of Nies, the proof of the undecidability of the Σ02 s-degrees yields a new proof of the known fact (due to Downey, LaForte and Nies) that the first order theory of the c.e. Q-degrees is undecidable.
Research Interests:
Research Interests:
Research Interests:
Research Interests:
Research Interests:
We show that in the language of fg, the ƒ3-fragment of the flrst order theory of the §02-enumeration degrees is undecidable. We then extend this result to show that the ƒ3-theory of any substructure of the enumeration degrees which... more
We show that in the language of fg, the ƒ3-fragment of the flrst order theory of the §02-enumeration degrees is undecidable. We then extend this result to show that the ƒ3-theory of any substructure of the enumeration degrees which contains the ¢02-degrees is undecidable.
We show that the rst order theory of the 0 2 s-degrees is undecid- able. Via isomorphism of the s-degrees with the Q-degrees, this also shows that the rst order theory of the 0 2 Q-degrees is undecidable. Together with a result of Nies,... more
We show that the rst order theory of the 0 2 s-degrees is undecid- able. Via isomorphism of the s-degrees with the Q-degrees, this also shows that the rst order theory of the 0 2 Q-degrees is undecidable. Together with a result of Nies, the proof of the undecidability of the 0 2 s-degrees yields a new proof of the known fact (due to Downey, LaForte and Nies) that the rst order theory of the c.e. Q-degrees is undecidable.
Research Interests:
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... more
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.
Research Interests:
Research Interests:
We show that every nonzero enumeration degree bounds a nonsplitting nonzero enumeration degree.