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Results tagged with computability-theory
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user 26705
computable sets and functions, Turing degrees, c.e. degrees, models of computability, primitive recursion, oracle computation, models of computability, decision problems, undecidability, Turing jump, halting problem, notions of computable randomness, computable model theory, computable equivalence relation theory, arithmetic and hyperarithmetic hierarchy, infinitary computability, $\alpha$-recursion, complexity theory.
2
votes
What are the most attractive Turing undecidable problems in mathematics?
Note that any set of intermediate Turing degree must lie in $L$; so I nominate the least such, with respect to the canonical ordering of $L$.
I suppose this set might have already been mentioned--it' …
9
votes
Accepted
Which reals are "hyperarithmetic modulo ordinals"?
In fact $\Delta^{1, ord}_1 = \mathbb{L} \cap \mathbb{R}$.
For suppose $(\phi(x, \overline{y})$, $\psi(x, \overline{y})$, $\overline{\alpha})$ is as you describe, defining $r \subset \omega$. We show …
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