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The phrase "any criterion that" is correct and usable in written English.
It can be used when discussing specific standards or principles that are applicable in a given context.
Example: "We must evaluate the project based on any criterion that ensures its success."
Alternatives: "any standard that" or "any measure that".
Exact(3)
A rule of gold uniquely befits the art business, whose material goods, by any criterion that is not strictly subjective, are worthless.
Any criterion that focuses on the question what entities need to be among the values of the variable 'x' in order for this sentence to be true?—appears to get the ontological commitments of the sentence wrong (see Rayo 2007 431 22007 431 2
Exclude any criterion that interview respondents regarded as desirable rather than essential.
Similar(57)
In later years, when the value of proportion and ornament became highly controversial, architectural theorists tended to avoid committing themselves to any criteria that might be subsumed under the heading venustas.
Beyond the uniform minimum requirements for admission, a program may choose any criteria that are appropriate as a basis for its evaluation, including but not limited to undergraduate and graduate grade-point averages, work experience, test scores, letters of recommendation, and evidence of past achievements.
And if you think of any criteria that may belong on the list of consideration, please, comment and let me know.
It is possible to apply any criteria that define a CpG island to their genomic sequences and identify some islands.
Sponsors should pre-define the acceptance criteria prior to performing the pivotal analytical studies, and should justify any criteria that are unexpected.
Furthermore, the cells obtained do not fulfill any criteria that identify them as stem cells, that is, the ability for higher cell potency, such as multipotency.
We defined as correlates any criteria that could be construed as antecedent to, or an outcome of, a functioning sex life or criteria that were "a degree or so removed from explicit sexual behaviour" [ 15, p 293].
Although the clinician has overall responsibility for ensuring that it is safe to undergo PDT, having a checklist would also provide an opportunity for the nurses to highlight or challenge any criteria that are not followed.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com