# Tag Info

### Are there any existing problems that wouldn't be solvable with a halting oracle?

Just take a problem whose Turing degree is above $0'$, which is the degree of The Halting Oracle. In terms of the arithmetical hierarchy you want problems which are above $\Sigma^0_1$. Examples of ...
• 28k

• 4,697
Accepted

### Can a Turing machine be both decidable and undecidable relative to itself?

A Turing machine doesn't come with an oracle. The oracle comes from outside. Rather, an oracle Turing machine is a Turing machine that has a special way of accessing an oracle. When you run the Turing ...
• 268k
Accepted

### Is the set of languages recognized by a Turing machine with an oracle countable?

Every language can be accepted by a Turing machine with an appropriate oracle, for example an oracle for the very language you want to accept. So if you understand "languages recognized by a Turing ...
• 268k