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The phrase "achieved on their" is not complete and lacks context, making it difficult to assess its correctness in written English.
It could be used in contexts discussing accomplishments or results that are attributed to a group or individuals, but it needs additional information to be fully clear.
Example: "The goals were achieved on their own terms, reflecting their unique strategies."
Alternatives: "accomplished by them" or "realized through their efforts".
Exact(15)
Partnerships with associate organizations and the community can lead to interaction effects including collaborative advantage and the achievement of outcomes that neither organization could have achieved on their own [ 37].
Google's team announced they were "cautiously optimistic" that quantum supremacy could be achieved on their device, with more development.
This article presents an overview of this new type of membrane, with a focus on recent progresses achieved on their fabrication methods.
We compare theoretically the levels of consistency which are achieved on non-binary constraints to those achieved on their binary decomposition.
Their joint efforts on scheduling, subscription sales, and advertising resulted in more tickets sold and a better bottom line than most of the organizations would have achieved on their own.
"If you read their college essays, all of them had things about how if they weren't competing with each other, that's what's driven them to achieve things they wouldn't have achieved on their own," said John Jennings, a reconstructive surgeon.
Similar(45)
Excruciatingly old-fashioned, she does not aspire to anything beyond the mountain; her sole mission is the care and emotional support of her brother, her life entirely untouched by modern notions about what women might achieve on their own.
Conditional NDCs offered two emission-reduction targets: shallow ones that countries could achieve on their own, and steeper ones they could achieve if carbon markets or other international mechanisms were part of the final agreement.
So when two big, stinky rock bands combine their efforts for a larger purpose it's only going to garnish a larger outcome than either one could achieve on their own".
There's very little in life that any one person can achieve on their own.
I realized that if I can inspire someone to feel and achieve on their own, whatever their background, that for me was the greatest achievement of all.
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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