In a single evening, Scarf realized that he could directly translate the Lemke-Howson s algorithm through a limiting process into an elementary and constructive proof of his core existence theorem.
32.
However, in general, the theorem is only an existence theorem, and does not provide any way for computing the solution, unless if one has an algorithm for computing the coefficients of B�zout's identity.
33.
He is known for his work on the embedding problem in algebraic number theory, the B�yer Neukirch theorem on special values of L-functions, arithmetic Riemann existence theorems and the Neukirch Uchida theorem in birational anabelian geometry.
34.
A typical application is furnished by the Arzel? Ascoli theorem or the Peano existence theorem, in which one is able to conclude the existence of a function with some required properties as a limiting case of some more elementary construction.
35.
The " existence theorem " for the twisted inverse image is the name given to the proof of the existence for what would be the counit for the comonad of the sought-for adjunction, namely a natural transformation
36.
The theorem also leads to the Grothendieck existence theorem, which gives an equivalence between the category of coherent sheaves on a scheme and the category of coherent sheaves on its formal completion ( in particular, it yields algebralizability .)
37.
Additionally, there should be at least a possibility ( if not a guarantee ) that the partner receives more than 1 / " n "; this explains the importance of the existence theorems of super-proportional division.
38.
It for example brings into question any use of Landau notation and its implied constants : are assertions pure existence theorems for such constants, or can one recover a version in which 1000 ( say ) takes the place of the implied constant?
39.
It was first proved by Kurt G�del in 1929 . It was then simplified in 1947, when Leon Henkin observed in his Ph . D . thesis that the hard part of the proof can be presented as the Model Existence Theorem ( published in 1949 ).
40.
A controversy that goes back to the early twentieth century concerns the issue of purely theoretic existence theorems, i . e ., theorems depending on non-constructive foundational material such as the axiom of infinity, the axiom of choice, or the law of excluded middle.
