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Parameter Definability in the Recursively Enumerable Degrees
"... The biinterpretability conjecture for the r.e. degrees asks whether, for each sufficiently large k, the # k relations on the r.e. degrees are uniformly definable from parameters. We solve a weaker version: for each k >= 7, the k relations bounded from below by a nonzero degree are uniformly defin ..."
Abstract

Cited by 38 (14 self)
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The biinterpretability conjecture for the r.e. degrees asks whether, for each sufficiently large k, the # k relations on the r.e. degrees are uniformly definable from parameters. We solve a weaker version: for each k >= 7, the k relations bounded from below by a nonzero degree are uniformly definable. As applications, we show that...
The Turing Universe Is Not Rigid
"... A nontrivial automorphism of the Turing degrees is constructed. ..."
Abstract

Cited by 6 (2 self)
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A nontrivial automorphism of the Turing degrees is constructed.
Clockwork or Turing U/universe?  Remarks on Causal Determinism and Computability
"... The relevance of the Turing universe as a model for complex physical situations (that is, those showing both computable and incomputable aspects) is discussed. Some wellknown arguments concerning the nature of scientific reality are related to this theoretical context. ..."
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The relevance of the Turing universe as a model for complex physical situations (that is, those showing both computable and incomputable aspects) is discussed. Some wellknown arguments concerning the nature of scientific reality are related to this theoretical context.