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searching for Computable set 7 found (324 total)

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

In his first theorem, Gödel showed that any consistent system with a computable set of axioms which is capable of expressing arithmetic can never be complete:

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

prefix-free Kolmogorov complexity is as low as possible, close to that of a computable set. Solovay proved in 1975 that a set can be K-trivial without being computable

Hilbert's tenth problem (3,277 words) [view diff] exact match in snippet view article find links to article

p(a,x_{1},\ldots ,x_{k})=0} provide a Diophantine definition of a non-computable set. Let A {\displaystyle A} be an algorithm that outputs a sequence of

Rice's theorem (1,712 words) [view diff] exact match in snippet view article find links to article

contradiction that P {\displaystyle P} is a non-trivial, extensional and computable set of natural numbers. There is a natural number a ∈ P {\displaystyle a\in

Well-structured transition system (1,037 words) [view diff] exact match in snippet view article find links to article

compatible, with respect to ≤ {\displaystyle \leq } ) and in addition has a computable set of minima for the set of predecessors of any upward closed subset of

Ordinal notation (1,889 words) [view diff] no match in snippet view article find links to article

O {\displaystyle {\mathcal {O}}} denotes a canonical (and very non-computable) set of notations. It uses a subset of the natural numbers instead of finite

Post's theorem (3,832 words) [view diff] exact match in snippet view article find links to article

jumps of the empty set. (The empty set could be replaced with any other computable set without changing the truth of the theorem.) Post's theorem states: A