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The names in a group of names must be distinct. Can the phrase 'over the names' be used to describe this restriction?

My sentence currently is "The name should be unique over all the names in the group". I'm not sure if this is correct usage.

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    Unique within the group is normal English. "Over the domain" is math jargon that is easy to understand, but still techie talk. Jul 27, 2021 at 11:09
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    What @YosefBaskin said. I'd also be okay with among or across the group in this context, but according to this NGram, only the first of those alternatives actually occurs as often as within. The words all the names in seem pointlessly redundant in the cited context. Jul 27, 2021 at 11:15

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I'm not entirely sure from your question whether you mean that the heading title should differ from all the other names within the group. Or whether you mean that just every name within the group must be different. So, let's try both!

If you have say four names and they must all be different then you could use the term 'throughout the group'. As in 'Throughout the group, all names must be unique'. Or, 'throughout each group all names must be unique'.

If you have an overarching name for the group - from which all sub-names must differ - then I would consider using those terms - overarching and sub - because they're very clear.

Then you could say 'all names in the subgroup must differ from the overarching group name.' (and add 'and from each other' if you like).

Overarching Definition adj. Forming an arch overhead or above. adj. Encompassing, extensive, or general. adj. Forming an arch (over something).

Source: Wordnik

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