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The phrase "a shared set" is correct and usable in written English.
It can be used to refer to a collection or group of items, ideas, or values that are collectively held or agreed upon by a group of people.
Example: "In our team meetings, we often discuss the importance of establishing a shared set of goals to ensure everyone is aligned."
Alternatives: "a common collection" or "an agreed-upon group".
Exact(59)
You need bonds beyond sex: a community, a culture, a shared set of obsessions.
"We had a shared set of interests and similar experiences," he said.
Build a shared set of measurable criteria that you believe depict a viable solution.
He's reveling in a shared set of values that transcend the rancor of this era.
Those findings and the conclusion that all human beings have a shared set of facial expressions remains unchallenged.
The loss of a shared set of values leads to a decline in tolerance, compassion and respect.
Keynes understood that a shared set of national cultural values is a strong defence against the ideology of laissez faire.
Hayek argued that without a shared set of values, the planners would inevitably impose some set of values on society.
Soil classification is a means of grouping soils into categories according to a shared set of properties or characteristics that will exhibit similar engineering behaviour under loading.
However, these associations cannot clarify whether this relationship is causal or due to a shared set of causal factors or even confounding.
Similar(1)
The pair definitely have a unique brotherly connection a shared set of references, inflections, and philosophies.
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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