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The phrase "established a basis for" is correct and usable in written English.
You can use it when discussing the foundation or groundwork for a concept, theory, or argument. Example: "The research conducted over the past decade has established a basis for understanding the effects of climate change on marine ecosystems."
Exact(12)
In announcing Friday that Israelis and Palestinians had established "a basis" for resuming direct peace negotiations, Mr. Kerry included a caveat.
THE research into co-rumination has looked only at symptoms of depression and anxiety over short periods and has not established a basis for predicting long-term negative effects.
In his seven years of power as first secretary and premier, he broke both the fact and the tradition of the Stalin dictatorship and established a basis for liberalizing tendencies within Soviet communism.
The Police Department has examined the officer's previous arrests and has not established a basis for additional charges, said Paul J. Browne, the department's chief spokesman; prosecutors in the Staten Island district attorney's office are still conducting a review.
In view of the Court of Appeals' unanimous decision that Microsoft illegally maintained its monopoly over PC-based operating systems -- the core allegation in the case -- the department believes that it has established a basis for relief that would end Microsoft's unlawful conduct, prevent its recurrence and open the operating system market to competition.
Narrowing the focus to this group established a basis for random sampling in front of polling stations across the UK.
Similar(48)
Kerry said he and the parties "reached an agreement that establishes a basis for direct final status negotiations".
Ms. Lagarde's reversal is a "welcome change in thinking, emphasizing that we should be establishing a basis for growth".
Later he improved several instruments and invented others without, however, establishing a basis for their commercial exploitation.
Getting to know any Iraqi enough to establish a basis for trust meant that some of this truth would eventually begin seeping out.
As with any documents presented as evidence, including police reports and findings from medical examiners, prosecutors must establish a basis for the credibility of the articles in court.
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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