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The phrase "allowed the establishment" is correct and usable in written English.
It can be used in contexts where permission or approval is given for the creation or formation of something, often referring to institutions or organizations.
Example: "The new policy allowed the establishment of community centers in underserved areas."
Alternatives: "permitted the creation" or "facilitated the formation".
Exact(57)
Beginning with New York in 1835, state laws allowed the establishment of free libraries supported by taxes and associated with school districts.
It professed to guarantee Tibetan autonomy and religion but also allowed the establishment at Lhasa of Chinese civil and military headquarters.
The traffic soon grew too great for the quays, and in 1663 Parliament allowed the establishment of alternative "sufferance wharves" on both banks.
In mid-1985 a new banking law allowed the establishment of new commercial banks to replace the publicly owned institutions (with the exception of an Islamic bank established in 1983) that had existed under the Touré government.
Such drastic changes in climate have sorted and resorted plant species, allowed the establishment of a diversity of forest types over time, and worked against the establishment or preservation of the mutual dependencies among species so common in the tropics.
The postliberalization period allowed the establishment of several private commercial banks and an overall expansion in banking, particularly with the government's decision in 1979 to allow foreign banks to open branches in Sri Lanka.
The ambiguous terms of the UN resolution 1973, which allowed the establishment of a "no-fly zone" to translate into a fully fledged air campaign, coupled with the failure of Russia and China to use their veto, allowed the First World's most advanced military machine to systematically destroy one from the Third World.
The enlarged state income allowed the establishment of a fixed budget that paid for 25,000 hired troops, as well as of a civil administration that also had control over churches and schools, a national army of 40,000 men, and a new navy to compete with Denmark's.
Similar(3)
Turkish officials announced, "We will never allow the establishment of a terror state along our borders".
It allows the establishment of minimum premium interest rates for country credit risk.
A pledge to allow the establishment of such schools formed a key part of the Conservatives' election manifesto.
More suggestions(17)
allowed the formation
allowed the institution
allowed the preparation
permitted the establishment
allowed the implementation
enabling the establishment
allowed the creation
permit the establishment
facilitating the establishment
possible the establishment
allowed the settlements
allowed the building up
allowed the institutions
allowed the schools
allowed the setting
enables the establishment
followed the establishment
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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