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The phrase "a theory consistent with" is correct and usable in written English.
It can be used when discussing a theory that aligns or agrees with certain principles, facts, or other theories.
Example: "The new findings provide evidence for a theory consistent with the established laws of physics."
Alternatives: "a theory in agreement with" or "a theory that aligns with".
Exact(3)
Still, Appel offered a theory consistent with the debate surrounding it.
A theory, like phrenology, that argued, with scientific evidence, that mental contents are innate was a theory consistent with the belief in a divine creator.
In the new study, Audoly and the MIT researchers have gotten together to produce a theory consistent with the experimental results.
Similar(57)
A mechanistic theory consistent with our findings holds that the development of asthma can be causally associated with the chronic effects from exposure to SHS on bronchial hyperreactivity rather than the acute effects of SHS exposure on airway caliber (Halken et al. 1995; U.S. EPA 1992).
Not only is endorsing a moral error theory consistent with the continued use of moral terms (as in "Nothing is morally wrong"), it is even consistent with the continued use of atomic moral claims (such as "Stealing pears is wrong").
This is important because it illuminates how turning to an explicit just peace theory consistent with Gospel nonviolence is central to incorporating both the constructive and obstructive programs, i.e. more fully becoming "peacebuilders" or as Pope Francis says "peacemakers".
Although Hoyle was forced to alter some of his conclusions, he tenaciously tried to make his theory consistent with new evidence.
In the succeeding paper, relevant experimental data will be interpreted according to the theory consistent with these observations.
The theory, consistent with what was later named (non-radical) constructivism, was that children, in suitable carefully arranged circumstances, can build their own knowledge of mathematics.
► Results inconsistent with configural theory, consistent with hierarchical theory.
For the authors, this implies identifying theory consistent with social science knowledge and theory.
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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