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searching for Computably enumerable set 7 found (15 total)

alternate case: computably enumerable set

Kleene's O (2,310 words) [view diff] exact match in snippet view article find links to article

{\mathcal {O}}} ; and given any notation for an ordinal, there is a computably enumerable set of notations which contains one element for each smaller ordinal

Diophantine set (1,475 words) [view diff] exact match in snippet view article find links to article

Matiyasevich–Robinson–Davis–Putnam or MRDP theorem, says: Every computably enumerable set is Diophantine, and the converse. A set S of integers is computably

Hilbert's program (1,158 words) [view diff] exact match in snippet view article find links to article

complete, consistent extension of even Peano arithmetic based on a computably enumerable set of axioms. A theory such as Peano arithmetic cannot even prove

Computation in the limit (1,678 words) [view diff] no match in snippet view article find links to article

{\displaystyle {\hat {r}}(x)} . As 0 ′ {\displaystyle 0'} is a [computably enumerable] set, it must be computable in the limit itself as the computable function

Reduction (computability theory) (1,982 words) [view diff] exact match in snippet view article

introduced by Post (1944). Post was searching for a non-computable, computably enumerable set which the halting problem could not be Turing reduced to. As he

K-trivial set (1,837 words) [view diff] exact match in snippet view article find links to article

function construction was due to Kučera and Terwijn. They built a computably enumerable set that is low for Martin-Löf-randomness but not computable. Their

Number theory (10,793 words) [view diff] exact match in snippet view article find links to article

Diophantine equations. In particular, this means that, given a computably enumerable set of axioms, there are Diophantine equations for which there is