Immerman and Vardi showed PTIME corresponds to least fixed-point logic only on ordered structures, revealing that logical captures are encoding-relative, not intrinsic to the complexity class.

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Encoding-relative(as describing what properties of complexity classes actually are): Dependent on how you choose to represent or format the information, rather than being a fixed property that works the same way no matter how you present it.
Immerman and Vardi(namesake of the theorem being discussed): Two computer scientists who proved an important theorem in the 1980s showing that certain logical systems can describe exactly the same problems as a famous computational complexity class.
Intrinsic to the complexity class(as the contrasting alternative to encoding-relative): A built-in, unchanging property of a category of computational problems that exists independently of how you represent those problems.
Least fixed-point logic(as a logical system): A type of mathematical language used to describe computational problems, built around the idea of finding the smallest set of solutions that satisfy certain repeating conditions.

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