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The phrase "a progressive escalation in" is correct and usable in written English.
It can be used to describe a situation where something increases or intensifies gradually over time.
Example: "The report highlighted a progressive escalation in tensions between the two countries over the past year."
Alternatives: "a gradual increase in" or "a steady rise in".
Exact(1)
We hypothesized that a progressive escalation in cell dosage might lead to a progressively enhanced therapeutic effect.
Similar(59)
"On the other hand, with some of these cases in hindsight it seems like a progressive escalation.
Progressive escalation of antibiotic resistance in MRSA has resulted in a limited option for treatment [ 1].
A progressive increase in doses is recommended.
San Francisco is a progressive city in an unforgivingly individualist nation.
"They mark a dangerous escalation in the crisis.
But the dead cats were a marked escalation in intimidation.
In recent months, the war between humans and seagulls has seen a dramatic escalation in violence.
"But it would lead to a dramatic escalation in the prevalence of Alzheimer's disease".
His letter represents a sharp escalation in the row between Miliband and the Mail group.
"But we're not seeing a rapid escalation in vineyard values".
More suggestions(1)
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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