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Results tagged with computability-theory
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user 120914
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.
9
votes
Accepted
Is the isomorphism problem solvable for torsion-free groups?
Novikov's centrally-symmetric group $\mathfrak{A}_P$ is a torsion-free group with undecidable word problem, constructed in [1]. Novikov did not prove it is torsion-free but, as Adian points out in [Ad …
4
votes
Accepted
Examples of "natural" finitely generated groups with an undecidable conjugacy problem
Chuck Miller in [Miller, Charles F., III On group-theoretic decision problems and their classification. Annals of Mathematics Studies, No. 68. Princeton University Press, Princeton, N.J.; University o …
17
votes
Decision problems for which it is unknown whether they are decidable
The word problem for a finitely presented group $G = \langle A \mid R \rangle $ and the associated canonical homomorphism $\pi : F_A \to G$, asks: given an element $w \in F_A$, do we have $\pi(w) = 1$ …