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Results tagged with computability-theory
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user 9550
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.
3
votes
What are the most attractive Turing undecidable problems in mathematics?
Say that an algorithm is reliable if given a string $S$ and integer $N$, it either halts and prints $|S|>N$ (meaning that Kolmogorov complexity of the string $S$ is greater than $N$) or does not halt, …
52
votes
What are the most attractive Turing undecidable problems in mathematics?
There is no algorithm that given positive integers $K$ and $x$ can decide if the following concrete Diophantine equation has a solution over positive integers:
\begin{align}
&(elg^2 + \alpha - (b-xy)q …
12
votes
1
answer
827
views
Transfinitely extending $\sf PA$ — can we get stronger than $\sf ZFC$?
Let $\sf PA$ denote the theory of natural numbers with constants $(0, 1)$ and binary operators $(+,\times)$ based on the first-order predicate calculus with equality, having the following axioms, wher …
- 6,819
28
votes
0
answers
905
views
On certain representations of algebraic numbers in terms of trigonometric functions
Let's say that a real number has a simple trigonometric representation, if it can be represented as a product of zero or more rational powers of positive integers and zero or more (positive or negativ …
- 6,819