proof independence

USAGE SUMMARY

The phrase "proof independence" is not standard in written English and may cause confusion.
It could be used in contexts related to mathematics or statistics, particularly when discussing the independence of proofs or results. Example: "In our research, we established proof independence to ensure that our findings were not reliant on a single method."

⚠ May contain grammatical issues

Human-verified similar examples from authoritative sources

Similar Expressions

60 human-written examples

In charge of this arrangement was the Bank of Latvia, with a bullet-proof independence, entrenched in law.The almost religious regard for the lat's stability echoed the arrangement in the pre-war republic, which stayed on the gold standard even after Britain abandoned it.

The Economist

Sometimes such results are called variants of Gödel's theorem, or their proofs of independence alternative proofs of Gödel's theorem, but this is misleading: interesting as they may be, they don't have the generality of Gödel's theorems proper, but only provide statements independent of a particular theory.

SEP

Lemma: Under our assumptions, Proof: by independence, cov(U,N) = where.

Emerging Infectious Diseases

Various answers to these questions have been found, including proofs of independence (based on the ordinary axioms employed in set theory) and proofs of conditional theorems made on the basis of certain familiar hypotheses of set theory.

Encyclopedia Britannica

Further, as a by-product of the proof-theoretic analysis we sometimes obtain simple independence proofs.

SEP

Mr. Romney pointed to his public record, his governorship of Massachusetts, as proof of his independence from his church.

The New York Times

Other candidates have made that work for them: Ross Perot and Michael Bloomberg practically throw their bankbooks on the table, as proof of their independence, and have been rewarded for it.

The New Yorker

Mr. Kasich, a former host of a conservative talk show on Fox News, received poor marks from the N.R.A. for supporting the assault weapons ban, which he points to as proof of his independence.

The New York Times

April 2, 1934 Long Branch, New Jersey March 23, 2007 Stanford, California Paul Joseph Cohen, (born April 2, 1934, Long Branch, N.J., U.S. died March 23 , 2007 Stanford, Calif.), American mathematician, who was awarded the Fields Medal in 1966 for his proof of the independence of the continuum hypothesis from the other axioms of set theory.

Encyclopedia Britannica

For a detailed account of the proof of the independence of the Axiom of Choice, see Bell 2005 or Jech 1973.

SEP

Industrial hardware verification flows lead to a requirement for automated proof of data independence without intrusion into the program, where the specification on which the proof is based makes no reference to details of the program language.

Electronic Notes in Theoretical Computer Science

Expert writing Tips

Best practice

When discussing mathematical or logical proofs, ensure that the term "proof independence" is clearly defined within the specific context to avoid ambiguity. Consider using more explicit alternatives.

Common error

Avoid using "proof independence" loosely to describe scenarios where proofs are merely different versions of the same argument. Ensure that the proofs genuinely operate on distinct axioms or methodologies.

Linguistic Context

The phrase "proof independence" functions as a noun phrase, potentially denoting a concept within mathematical logic or a similar field. Ludwig AI indicates that the phrase is not standard, suggesting it requires careful contextualization.

Expression frequency: Missing

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Ludwig's WRAP-UP

In summary, "proof independence" is a niche phrase, primarily relevant in technical fields like mathematical logic. Ludwig AI signals that the phrase isn't standard, advising caution in its usage. It aims to convey that a statement's truth can't be established based on a specific set of rules or axioms. Due to its potential for ambiguity, it's advisable to opt for more explicit alternatives such as "independence of axioms" or "unprovability from axioms" to ensure clarity. The absence of real-world examples further underscores the need for careful and context-specific application of the term.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

Demonstrating independence

Focuses on the act of showing independence rather than the evidence itself.

Establishing autonomy

Emphasizes self-governance or freedom from external control.

Verifying non-reliance

Highlights confirming that something does not depend on something else.

Confirming separateness

Emphasizes establishing a distinct or individual identity.

Validating self-sufficiency

Focuses on confirming the ability to function without external assistance.

Proving non-correlation

Highlights the absence of a statistical relationship between variables.

Evidence of sovereignty

Shifts the focus to demonstrating supreme authority or freedom from external control.

Independent verification

Highlights that the verification process is done independently.

Independent validation

Highlights that the validation process is done independently.

Confirming proof autonomy

Highlights the existence of autonomous proofs.

FAQs

What does "proof independence" mean in the context of mathematical logic?

In mathematical logic, "proof independence" refers to the property where a statement can neither be proven nor disproven from a given set of axioms. This is often demonstrated through techniques like forcing.

How can I demonstrate "demonstrating independence" of a result?

Demonstrating the independence of a result typically involves constructing models or using techniques like forcing to show that the result holds in some models but not in others, relative to a specific set of axioms.

What are some alternatives to saying "proof independence"?

Alternatives include "independence of axioms", "unprovability from axioms", or specifying that a statement is "independent of a particular theory".

Is there a difference between "proof of independence" and "proof independence"?

"Proof of independence" is the more common and grammatically standard phrase, referring to a demonstration that a statement is independent of a set of axioms. "Proof independence" is less common and may cause confusion.