例句與造句

1. However it does not have a recursively enumerable set of axioms, and thus does not satisfy the hypotheses of the incompleteness theorems.
2. A more general class of sets consists of the recursively enumerable sets, also called "'semidecidable "'sets.
3. This can be used to give a rigorous proof of G鰀el's first incompleteness theorem, because no recursively enumerable set is productive.
4. The proof above shows that for each recursively enumerable set of axioms there is a recursive set of axioms with the same deductive closure.
5. Matiyasevich showed this problem to be unsolvable by mapping a Diophantine equation to a recursively enumerable set and invoking G鰀el's Incompleteness Theorem.
6. It's difficult to find recursively enumerable set in a sentence. 用recursively enumerable set造句挺難的
7. The theory of algebraically closed fields of a given characteristic is complete, consistent, and has an infinite but recursively enumerable set of axioms.
8. Very soon after this, Friedberg and Muchnik independently solved Post's problem by establishing the existence of recursively enumerable sets of intermediate degree.
9. The fundamental results establish a robust, canonical class of computable functions with numerous independent, equivalent characterizations using Turing machines, lattice of recursively enumerable sets.
10. Also, since all functions in these languages are total, algorithms for recursively enumerable sets cannot be written in these languages, in contrast with Turing machines.
11. Much recent research on Turing degrees has focused on the overall structure of the set of Turing degrees and the set of Turing degrees containing recursively enumerable sets.
12. This groundbreaking result opened a wide study of the Turing degrees of the recursively enumerable sets which turned out to possess a very complicated and non-trivial structure.
13. In computational complexity theory, the complexity class containing all recursively enumerable sets is lattice of r . e . sets under inclusion is denoted \ mathcal { E }.
14. But Post left open the main problem of the existence of recursively enumerable sets of intermediate Turing degree; this problem became known as " Post's problem ".
15. The theory of first-order Peano arithmetic is consistent, has an infinite but recursively enumerable set of axioms, and can encode enough arithmetic for the hypotheses of the incompleteness theorem.
16. If one takes all statements in the language of Peano arithmetic as axioms, then this theory is complete, has a recursively enumerable set of axioms, and can describe addition and multiplication.
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