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Discover LudwigThe phrase "assert their claim over" is correct and usable in written English.
It can be used when discussing the act of declaring or maintaining a right or ownership over something, often in legal or formal contexts.
Example: "The company sought to assert their claim over the patent after the recent court ruling."
Alternatives: "establish their right to" or "maintain their ownership of".
Exact(1)
European officials moved quickly to assert their claim over the leadership of the International Monetary Fund on Thursday, suggesting a serious challenge is being mounted by emerging economic powers like China and India that believe the time has come to break Europe's historic grip on the post.
Similar(59)
Our troops handle Iraq's valves in an endless process of managing sectarian tensions, while working to keep regional rivals from asserting their claim over Iraq's sovereignty.
Others assert their claim to the neighborhood's First Family more insistently.
Further, appellants are not being forced to assert their claims in a criminal prosecution.
Accordingly, the Court allowed appellants to assert their claims in an equitable proceeding.
Many urban refugees attempted to assert their claims either through protesting or other collective means.
These histograms would ideally reflect a clear bimodal distribution and would allow the authors to more clearly assert their claims.
The Russians, it was assumed, were asserting their claim, perhaps even launching a scramble for Arctic resources.
But both are vigorously asserting their claims to the presidency and cobbling together possible coalitions in the new Parliament.
As David Sanger observed at the beginning of the month, "as the Chinese grow more determined to assert their territorial claims over a string of islands once important mainly to fishermen, America's allies are also pouring military assets into the region -- potentially escalating the once obscure dispute into a broader test of power in the Pacific".
Regional powers would vie for pre-eminence and assert their historic claims.
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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