The type of regularity of a group of statements (i.e., how it is regulated, caught up in a system of discursive rules) differs from one discursive formation to the next. Two statements may be homogeneous in terms of grammar and logic, but different in their enunciative regularities. Thus, 'enunciative homogeneity' is not tied down to linguistic or logical identity, although it may intersect with them in complex ways.
All this does not mean that archeology cannot describe hierarchies of statements within a given discourse. Such a hierarchy or 'tree of derivation' would place at the top (the 'root') statements that set out broad rules for the practice of the discourse; at the bottom (the tips of the branches) would be statements with a more specific range (technical improvements, minor 'discoveries,' etc). But this archeological hierarchy is autonomous both from hierarchies of deductive systems (in which one statement depends on another, more general one) and chronological hierarchies (in which later statements derive from earlier ones); it may intersect with these other hierarchies, but it is of a different 'order' altogether.
Part III ends with a brief description of the archive, the level at which discursive formations (and the statements of which they are comprised) are put in relation to the practice of the historian. In Part IV, Foucault moves further into the realm of historical practice, attempting to show how the field he has defined leads to a unique kind of history. Foucault is testing, then, 'whether [his] machine works, and what it can produce.' More specifically, he is addressing the issue of whether it can produce something new.
The biggest threat here is the history of ideas, a form of history that seems dangerously close to what Foucault's new method would end up describing. Thus, the bulk of Part IV is a critique of the history of ideas, showing its difference from Foucault's 'archeological method.' In Chapter 1, Foucault sets out four 'principles' that limit and define what archeology can do. For the most part, these principles are by now familiar: they all define Foucault's method as one that describes nothing but discourse itself (not a hidden spirit of the times, not a broad, totalizing historical progression, not a psychology, and not points of innovation or origin).
This total dismissal of discourse as something that 'points to' or describes something else has a significant resonance in Foucauldian terms like 'archeology' or 'monument.' Such terms remind us that he is describing discourse almost as an archeologist would describe a physical artifact; although the artifact is distant from our own time, it can be described objectively in great detail, without speculation as to its inner meaning. Again, despite all of Foucault's often vindictive criticisms of other kinds of history or analysis, he never claims that the archeological method tells us everything we might want to know. Other methods simply say something different.
Although most of the principles laid out in this chapter echo principles repeated throughout the book, Foucault pushes his insistence on a positive, fully describable field toward an extreme here. He insists that the archeological method does not seek any kind of return to past events, any kind of discovery of the moment of birth of a given statement. It is in this context that he makes the claim (quoted above) that his method is 'nothing more than a re-writing.' Such a historical practice would be quite radical, since it would claim to do nothing but re-present the archive in a new form. This possibility haunts Foucault now and again, because it would mean that his own written histories are of the same order as the statements they describe. Foucault's own texts would thus become just another part of the vast, anonymous field of discourse. For now, however, this existential issue is left aside.