Sentence examples for made essential use from inspiring English sources

The core of Cohen's method of proof the celebrated method of forcing was vastly more general than any previous technique; nevertheless his independence proof also made essential use of permutation and symmetry in essentially the form in which Fraenkel had originally employed them.

"Not only can this procedure be repeated any finite number of times, it can also be iterated into the transfinite". Feferman investigated how far into the transfinite such progressions could be carried, and established fundamental completeness and incompleteness results for them, depending on the way that they are generated; these results made essential use of his work on arithmetization.

Dirac's attempt to prove the equivalence of matrix mechanics and wave mechanics made essential use of the delta function, as indicated above.

As the debate concerning the Axiom of Choice rumbled on, it became apparent that the proofs of a number of significant mathematical theorems made essential use of it, thereby leading many mathematicians to treat it as an indispensable tool of their trade.

The known proofs on the symmetric Fock space make essential use of the Nevanlinna Pick properties.

Foucault is, then, right: psychiatric practice makes essential use of moral (and other evaluative) judgments.

The construction makes essential use of the representation of CFT tensor operators as polynomials in an auxiliary polarization tensor.

To overcome this difficulty, we make essential use of the concept of two-scale Young measures for algebras with mean value, associated with bounded sequences in L2.

The new calculus is termed the λσβ0-calculus, since it makes essential use of an extension of β0-unification (described in another paper).

Our proofs make essential use of techniques based on a logarithmic Sobolev inequality, Rosen's inequality (proved via a new Fenchel Young inequality), and a very precise asymptotic formula due to Hartman and Wintner.

The foregoing argument makes essential use of collapse.