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The phrase "a common set of terms" is correct and usable in written English.
You can use it when referring to a shared vocabulary or terminology that is understood by a specific group or in a particular context.
Example: "In our discussions, we need to establish a common set of terms to ensure everyone is on the same page."
Alternatives: "a shared vocabulary" or "a standard terminology".
Exact(3)
A common set of terms and definitions of online and blended learning compiled for the Online Learning Consortium Mayadass & Miller, 2014) is an attempt to classify most of the varieties.
However, where interoperability between applications is important, the community will come in time to settle on a common set of terms that can be implemented across all the relevant packages.
Where controlled vocabularies provides a basic level of interoperability by providing a common set of terms for communication between both machines and humans the Information Model improves interoperability by means of an ontology that provides semantic information or additional related context for the terms.
Similar(55)
Such a comparative analysis is made possible by the fact that genes from different species are annotated using a common set of GO terms.
We also identified an enrichment of a common set of GO terms associated with genes showing parent-of origin effects with maternal-like transcript levels, many of which are involved in development and differentiation (Additional file 1: Table S1).
However, the field would benefit if a common set of domain terms could be adopted to form the core of the needs assessments, and if items could be placed uniformly within domains.
As an alternative evaluation approach for unlabeled trees, we quantified 'correctness' in terms of the agreement between the topologies of plain trees and reference trees (pruned to a common set of leaves) in terms of the Robinson Foulds distance [ 32].
In addition, all the terms and the database employed in the STD evaluation held in 2014 were kept, enabling a comparison between the systems submitted to both evaluations on the common set of terms.
Using a common set of outcome tools and adopting the operational terms presented in this paper to allow comparison across studies.
Likewise I think the iPhone has been very successful in terms of having a common set of controls and metaphors to program against.
Therefore, it appears that although some GO terms were enriched with more than one of the proteins, it is not because these proteins bound to a common set of messages that connects to one particular GO term, but rather that they were associated with different messages that belong to the same functional class.
More suggestions(17)
a common set of concerns
a common set of rules
a single set of terms
a rich set of terms
a curated set of terms
a common vocabulary of terms
a standard set of terms
a different set of terms
a particular set of terms
a similar set of terms
a broad set of terms
a standardized set of terms
a separate set of terms
a strict set of terms
a curious set of terms
a predefined set of terms
a common understanding of terms
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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