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The phrase "established the basis" is correct and usable in written English.
You could use it in a sentence like this: "The groundbreaking research established the basis for a new understanding of the problem."
Exact(53)
Thus, the New Testament established the basis for the doctrine of the Trinity.
His conquest of the leading Sudanese trading cities established the basis for Songhai's future prosperity and expansion.
His plan helped save the convention from disintegrating and established the basis of the present system of federal government.
Certainly, through its legacy of science and reason, the Enlightenment established the basis for two centuries of Western -- American and European -- hegemony over the definition of civilization.
Otakar's reign thus established the basis of a strong Bohemian state, which was to reach the height of its power later in the 13th century.
In Book I he established the basis for a mathematical treatment of spherical triangles analogous to Euclid's treatment of plane triangles.
Similar(6)
Usually the victim has to give evidence in court to establish the basis for a prosecution.
First, we've been establishing the basis for using various tree species in Guatemala for dendrochronology.
As the trial closed last week, he accused both women of lying about the attacks to establish the basis for lawsuits.
The party would be short-lived, but its example would establish the basis for populism in the United States and Europe.
But establishing the basis can be messy, Mr. Nicholson noted, when people invest through dividend reinvestment plans.
More suggestions(18)
established the foundation
established the groundwork
established the ground
determined the basis
established the rationale
established the backbone
tested the basis
established the basic
established the reason
formation the basis
established the starting point
established the cornerstones
established the bases
stated the basis
established the foundations
determine the basis
provided the basis
discovered the basis
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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