Sentence examples for proof of consistency from inspiring English sources

Although there remains the theoretical possibility of a finitary proof of consistency that cannot be reflected in the foregoing systems of set theory, no hopeful, positive results have been obtained.

Thus, a proof of consistency or of undecidability of a given sentence $\varphi$ is always a relative consistency proof.

Whittle's solution to the problem of estimating the parameters and the proof of consistency of parameters of the above sine wave used arguments which are not mathematically rigorous.

In his proof of consistency of parameters, he used the following O p result: max 0 ≤ ω ≤ π | ∑ t = 1 n Y t e i ω t | = O p ( n 3 4 ), where { Y t } is a linear process.

Another corollary was a syntactic proof of consistency: if a contradiction is provable, anything is provable, but an atomic formula, say, has no proof: if it has a proof, it has a normal proof, but no E-rules apply to an atomic formula, and no I-rule concludes it either.

But a crucial step in assessment of a new instrument is in general the proof of consistency of the measurement results, which is the task of the present study.

Hilbert's meta-proof of consistency, by contrast, Reichenbach thinks is genuinely important.

We end this consideration of the Second Incompleteness Theorem by noting that there are semantic proofs of consistency of course.

For Hilbert, the aims were a complete clarification of the foundational problems through finitary proofs of consistency, etc, aims in which proof theory failed.

But Gödel's 1938 proof of its consistency, relative to the consistency of ZF, dispelled any suspicions left about it.

In 1963, twenty-five yeafterfter Gödel's proof of the consistency of the CH, relative to the consistency of ZFC, and the consistency of the AC from the consistency of ZF, Paul Cohen (1966) proved the consistency of the negation of the CH, relative to the consistency of ZFC.