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The phrase "a further criterion for" is correct and usable in written English.
It can be used when discussing additional standards or benchmarks that are being introduced or considered in a particular context.
Example: "In evaluating the effectiveness of the program, we must establish a further criterion for success that includes participant feedback."
Alternatives: "an additional standard for" or "a supplementary measure for".
Exact(8)
This review investigated whether soft signs met a further criterion for an endophenotype, namely familial association.
A further criterion for identification was the presence of 3' UTRs located at the ends of operons.
As a further criterion for the differentiation of M. bovis, intrinsic resistance to pyrazinamide (PZA) has been described (2 ).
As a further criterion for LADA, we used information on insulin treatment (available for 82% of the participants) to separate LADA from classical type 1 diabetes.
A further criterion for judging success is containing student drop-out, which is frequently noted as very high in distance settings [ 10].
This systematic review and meta-analysis aimed to determine how far soft signs in schizophrenia met a further criterion for an endophenotype, namely familial association.
Similar(52)
We added a further criterion for the sRNAs that mapped to the genome with one mismatch.
A further criteria used for the selection of TILLING fragments was the probability of finding deleterious SNPs (mutations affecting splicing sites or introducing stop codons) considering the types of transition mutation generally induced by EMS treatment (G → A; C → T).
First of all, we consider the update of an action description with respect to further criteria, for instance, by ensuring that the updated description entails some observations, assertions, or general domain properties that constitute further constraints that are not expressible in an action description in general.
In this paper we focus on specific electrochemical reactions at the interface between the conducting polymer and the metal that were found to define further criteria for successful application.
Further criteria for selection of the miRs are provided in the "Results" section.
More suggestions(17)
a further approach for
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a further guideline for
a supplementary criterion for
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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