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The theory of the recursively enumerable weak truth-table degrees is undecidable

  • Klaus Ambos-Spies (a1), André Nies (a1) and Richard A. Shore (a2)


We show that the partial order of -sets under inclusion is elementarily definable with parameters in the semilattice of r.e. wtt-degrees. Using a result of E. Herrmann, we can deduce that this semilattice has an undecidable theory, thereby solving an open problem of P. Odifreddi.



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[ASp.Sh?]Ambos-Spies, K. and Shore, R., Undecidability and 1-types in the r.e. degrees (in preparation).
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[Od89]Odifreddi, P., Classical recursion theory, North-Holland, Amsterdam.
[So87]Soare, R. I., Recursively enumerable sets and degrees, Springer-Verlag, Berlin.


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