Computational complexity results are often explained in intuitive terms as statements about the possible efficiencies of algorithms to solve certain classes of problems.
However, on a more formal level, all (many?) results actually build on the underlying notion of Turing machines, which provides a precise way to define computation.
My question is then: can all computational complexity statements be fully expressed in terms of lines of (pseudo-)code?
If so, would that mean that one should state all results building on a finite set of "elementary operations" that are allowed in the programming language under consideration? What would be the "elementary operations" in such a context?