<p>Yes, there are intermediate degrees.  One way to see this is that there are computably enumerable sets that are Turing incomparable.  See <a href="https://secure.wikimedia.org/wikipedia/en/wiki/Turing_degree">https://secure.wikimedia.org/wikipedia/en/wiki/Turing_degree</a> for some basic information.</p>

CC BY-SA 2.5
2011-01-24T16:19:10.847Z
2011-01-24T16:19:10.847Z
kasterma
<p>are there systems whose nontrivial properties can't be decided by Turing machines, but for which a Turing machine with an oracle able to find out these properties isn't able to solve the Halting problem (for ordinary TMs)?</p>

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2011-01-24T17:21:18.637Z
I think this question is not research-level. Voting to close as off-topic.
Kaveh
CC BY-SA 2.5
2011-01-25T05:58:57.033Z
I think this is an okay question, although the wording is a little confusing.
Huck Bennett
<computability><turing-machines><halting-problem>
Undecidable problems not Turing-complete?
Laura
# Undecidable problems not Turing-complete?

(Asked by: username_0 on 2011-01-24)

are there systems whose nontrivial properties can't be decided by Turing machines, but for which a Turing machine with an oracle able to find out these properties isn't able to solve the Halting problem (for ordinary TMs)?

**Tags:** computability, turing-machines, halting-problem
> **Comments:**
> **username_1**: I think this question is not research-level. Voting to close as off-topic.  
> **username_2**: I think this is an okay question, although the wording is a little confusing.  

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## 1 answers

### Answer by username_3 on 2011-01-24. Score: 6 | Accepted answer

Yes, there are intermediate degrees. One way to see this is that there are computably enumerable sets that are Turing incomparable. See <https://secure.wikimedia.org/wikipedia/en/wiki/Turing_degree> for some basic information.


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