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Results tagged with computability-theory
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user 172527
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
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1
answer
155
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Sets $A$ such that $A$-maximal sets are $\Delta^0_2$
Recall that $M\subseteq\omega$ is maximal if it is c.e., and can be only trivially extended by other c.e. sets, i.e. if $M\subseteq N$ and $N$ is c.e., then either $\overline{N}$ or $N\setminus M$ is …
- 141
0
votes
Accepted
Sets $A$ such that $A$-maximal sets are $\Delta^0_2$
Turns out (as I suspected!) all such sets are $\Delta^0_2$, so that this property exactly characterizes lowness.
Fix an $A$-maximal $M$. For any $B\leq_T A$, one can build $C = \overline{M}\oplus_B\em …
- 141
2
votes
0
answers
92
views
Is there a nice characterization of degrees which compute no c.e.a. set?
Recall that a set $A$ is c.e.a. (computably enumerable in and above) if there is some $X<_T A$ such that $A$ is $X$-c.e.
I am interested in degrees (specifically $\Delta^0_2$ degrees) that are not onl …
- 141