Sentence examples for by a deep result from inspiring English sources

It turns out that (by a deep result of Magidor, published in 1977) GCH can first fail at ℵω (assuming the consistency of a supercompact cardinal).

However, one might counter this as follows: The higher degree of Ω-completeness in the case for ¬CH is really illusory since it is an artifact of the fact that under the theory of H ω2) is in fact mutually interpretable with that of H ω1) (by a deep result of Woodin).

This is unfortunately not clear (at least to the author), because of a deep result by Toledo [354], giving a negative answer to another question posed by Serre.

He also gave the first proof of the law of quadratic reciprocity, a deep result previously glimpsed by Euler.

A deeper result on the weak solution was obtained by Caffarelli et al. in [4].

This compound is characterized by a deep green colour that results from n → π* and π → π* transitions similar to those observed in diphosphenes.

A deep, fundamental result in flow dynamics is.

These results are then confirmed by a deep theoretical analysis based on the contraction mapping theory.

The result is the first great American novel underpinned by a deep understanding of the complexity of spin bowling.

Although a shorter proof has been given later by Cicalese and Leonardi [45] using the regularity theory for area minimizing sets of finite perimeter, the proof by symmetrization uses no deep results from geometric and functional analysis, is geometrically intuitive and can be adapted to other situations where a complete regularity theory is not available.

The first time Ireland embraced austerity, a deep recession resulted.