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The phrase "a higher order and" is grammatically correct and can be used in written English.
It can be used when discussing concepts that involve levels of complexity, hierarchy, or classification, often in academic or technical contexts.
Example: "The research aims to explore a higher order and more complex interactions between the variables involved."
Alternatives: "a greater level and" or "an elevated order and".
Exact(8)
Nureyev was the Brando of ballet, a solipsistic brute, an especially unusual character in a profession where obedience to a higher order and good manners are central to the art itself.
What we are left with, in short, is not only a devastating portrait of an Albert Speer who was at heart no different from any other of the Nazi leaders, but also a detailed analysis of how Speer managed to sell himself as the dispassionate technician whose guilt was somehow of a higher order and therefore more palatable.
XRD data showed that the diffraction peaks in the hybrids were narrower than those of the organoclay implying a higher order and more number of layers in the stacks of clays.
Now, owning your data could advance to a higher order and the consequences for humanity might just be priceless.
Without faith in a higher order and the existence of something outside ourselves and our everyday lives, life can become emotionally unbearable and filled with fear.
That takes the dialogue back and forth to the point where it begins to move toward a higher order, and the arguments become more sophisticated.
Similar(52)
Boulding conceptualized systems' interrelationships by stating that "all lower level systems are embedded in systems of a higher order [and become their sub-systems]...but higher level systems have unique characteristics".
Exhibitions at the Bibliothèque Nationale are commonly of a high order and require a modest entrance fee.
This is home cooking of a high order — and rarely has a restaurant made me feel more at home.
This is writing of a high order, and Berlinski demonstrates a continuous awareness of those heights — his conventionalities are superior to many writers' originalities.
Adlai E. Stevenson (Dem)., as legislator and State Treasurer, has demonstrated leadership qualities of a high order and would bring to the Senate a fresh and individual viewpoint.
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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