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The phrase "a criterion for the" is correct and usable in written English.
It can be used when discussing a standard or principle used to judge or evaluate something.
Example: "The researchers established a criterion for the selection of participants in the study to ensure a diverse sample."
Alternatives: "a standard for the" or "a benchmark for the".
Exact(60)
Every other child (49.9 %) reported an event that fulfilled the A criterion for the PTSD diagnosis based on DSM-IV.
If eccentricity was a criterion for the job, Bob was qualified.
And, if philanthropy becomes a criterion for the renaming of theatres, we may be going down a very rocky path.
The B.C.S. coordinator Mike Tranghese, who is also Big East commissioner, said that after the Nebraska imbroglio, the B.C.S. considered making winning a conference championship a criterion for the title game but could not reach a consensus.
In fact, a criterion for the pieces was that they had to be both "cow-friendly" and "cow-proof," said A. Eric Arctander, an artist and a co-founder of Collaborative Concepts.
A criterion for the first eigenvalue is proved.
So behavior is regarded as a criterion for the presence of mental states.
He also proposed a criterion for the uniform correctness of unbounded operator.
We also define the Rayleigh quotient and prove a criterion for the smallest eigenvalue.
Now we are ready to establish a criterion for the interior of a solid cone.
A criterion for the three-dimensional stress state is proposed to predict fatigue crack initiation angles.
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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