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The phrase "a higher order" is correct and usable in written English.
It can be used in contexts discussing levels of complexity, classification, or hierarchy in various fields such as mathematics, philosophy, or organizational structures.
Example: "In mathematics, a polynomial of a higher order can exhibit more complex behavior than a linear polynomial."
Alternatives: "a greater level" or "a superior rank".
Exact(34)
But Helen Fitzgerald's Viral is of a higher order.
It is a species leap, a higher order of being.
The art, too, is of a higher order.
There was some poetry, at least, of a higher order.
Monumental sculpture of a higher order is avidly sought after.
"I would call it civil disobedience of a higher order," she said.
Similar(26)
Is it a higher-order perception of one's mind's operation, or is it a higher-order thought about one's mental activity?
Our work establishes bismuth as a higher-order topological insulator.
Mansinghka, V., Selsam, D. & Perov, Y. Venture: a higher-order probabilistic programming platform with programmable inference.
With this method, we can define a class that behaves like a higher-order function.
A higher-order gradient continuum constitutive relationship is developed and incorporated into a higher-order Cauchy Born rule.
More suggestions(23)
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by a higher order energy
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a higher prescription
a broader order
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a higher procedure
a higher purpose
a higher request
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a rising order
a superior order
a higher level order
a higher prioritization
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a higher threshold
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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