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"on the readiness" is correct and usable in written English.
You can use it when you are referring to being prepared for something. For example: I need to work on my readiness for the upcoming exam.
Exact(46)
But mobility depends on the readiness of governments to allow access to foreign students.
The White House has conditioned further withdrawals of American troops on the readiness of the Iraqi military and police.
The talks between Athens and its creditors have centred on the readiness of the Tsipras government – a coalition of radical leftwingers and populist rightwingers – to liberalise the economy.
A recently released independent study of the Army found that recreation and family programs have a direct impact on the readiness and retention of soldiers.
The schedule and release date depend largely on the readiness of SpaceShipTwo, which is still being tested in the Mojave Desert.
Was this not supposed to be an alliance based on the readiness of senior Liberal Democrats and Tories to think the unthinkable in reforming the state?
Similar(11)
Our participants rated highly on the readiness-to-quit ladder, and reported high motivation to quit.
Three-quarters of participants were either in the 'preparation' or 'action stage' on the readiness-to-quit ladder.
Participants rated highly on the readiness-to-quit ladder, and reported high motivation to quit, which may not be generalisable to all hospitalised patients.
This paper focuses on verifying the readiness, feasibility, generality and usefulness of multi-staging programming in software applications.
This study focused on developing the readiness instrument for evaluation of the e-tutors, and hoped to assist the mentor to understand the teaching e-tutors well.
More suggestions(17)
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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