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The phrase "axiomatic comparison with" is correct and usable in written English.
It can be used in contexts where you are discussing a fundamental or self-evident comparison between two or more concepts or entities.
Example: "The axiomatic comparison with established theories highlights the validity of the new hypothesis."
Alternatives: "self-evident comparison to" or "fundamental comparison with".
Exact(1)
From the perspective of formal logic, Pearl's book offers the most comprehensive analysis, via an axiomatic comparison with Lewis's hierarchy of conditionals.
Similar(59)
Comparison with Mr. Coolidge.
Equally, the comparison with Militant is misleading.
Again, the comparison with Colombia is useful.
In comparison with men of golden talents,.
Comparison with mainland Europe is also gratifying.
The comparison with China is obvious.
The comparison with Japan and Europe is staggering.
Comparison with fr.
However, in comparison with Hillary, there is no comparison".
We made comparisons with Egypt.
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