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The phrase "a criterion necessary" is correct and usable in written English.
It can be used when discussing a specific standard or requirement that must be met in a particular context.
Example: "In order to qualify for the grant, applicants must meet a criterion necessary for funding approval."
Alternatives: "an essential criterion" or "a required standard".
Exact(1)
A second added value of our study was the exploration of a possible dose-effect relation, a criterion necessary to establish robust links between benzodiazepine use and risk of Alzheimer's disease.
Similar(59)
Most importantly, content validity has been established in this population, a key criterion necessary for FDA acceptance in supporting labeling claims.
Concerning the evaluation of the BRIPPA EQA as a revalidation method it should be indicated that such a scheme has partial confidentiality, multiple sources of data and assessors, and a sampling procedure over several time frames, fulfilling almost all criteria necessary for a revalidation method.
A criterion is necessary to determine the possibility of continuing use for the wall-thinned pipes detected by non-destructive inspection.
Therefore, a criterion is necessary to to decide whether the lever's compliance can be neglected or not.
Again, we selected items from the SMFQ a priori based on criteria necessary to establish a depression diagnosis and other research suggesting the stability of the items in depressed youth throughout childhood [ 30, 31].
Breast cancer (BC), as a disease, meets the criteria necessary for carrying out a population-based screening [ 1].
We defined potential synapses as axo-dendritic separations of <1 μm, a criterion that is necessary but not sufficient for a real synaptic connection (see Experimental Procedures).
Now, me calling you a racist under that description of racism isn't a value judgment about you personally (I don't even know you); it's merely an observation about the criteria necessary to establish that racism exists, and that otherwise nice folks (Christian or not) are up to their eyeballs in it.
Two of the country's leading judges yesterday paved the way for an important high court test case to examine the criteria necessary for an abortion to go ahead.
InstaPoC was created in compliance with the imaginatively-named PoC (Push to Talk over Cellular) 2.0 standard, which lays out in excruciating detail the criteria necessary for a reliable, business-grade push-to-talk system.
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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