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Results tagged with computability-theory
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user 130978
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.
6
votes
1
answer
226
views
Is there an injective homomorphism on the Turing degrees?
I know that the existence of a non-trivial automorphism of the Turing degrees is a long-standing open problem. I am curious to know if something is known about (non-trivial) injective homomorphisms (o …
- 342
4
votes
Understanding the definition of a (computably / continuously) “transparent” function
The intuition for transparency functions is the following (then all the other notions are slight variations): if you are trying to apply some $f$ after $U$, this is indeed the same as applying some ot …
- 342
3
votes
1
answer
170
views
Computing the halting problem with no computable bound on the use function
I would like to prove that there are two sets $A,B\subset \mathbb{N}$ such that
$A |_T B$
$\emptyset' \equiv_T A\oplus B$
for every $e$, if $\{e\}^{A\oplus B}=\emptyset'$ then the map sending $(B,n)$ …
- 342
1
vote
0
answers
97
views
Existence of limit computable map
Is there a limit computable function $\Phi$ with the following properties?
Let $T\subset \mathbb{N}^{<\mathbb{N}}$ be a tree (coded as its characteristic function) and $f\in\mathbb{N}^\mathbb{N}$ be …
- 342
5
votes
0
answers
157
views
The set of homogeneous solutions of a clopen contains an hyperarithmetical set
In the context of Galvin-Prikry generalization of Ramsey's theorem, I read in a couple of papers ([1],[2]) that Solovay [3] proved that if $P$ is a clopen of $[\mathbb{N}]^{\mathbb{N}}$ then the set o …
- 342