Having said, or at least implied, that we won’t be departing in this chapter from our usual assumptions regarding decomposition and recomposition operators, I’ll begin my discussion of sixth normal form by doing exactly that ... In our book *Temporal Data and the Relational Model* (Morgan Kaufmann, 2003), Hugh Darwen, Nikos Lorentzos, and I define:

Generalized versions of the projection and join operators, and hence

A generalized form of join dependency, and hence

A new normal form, which we call 6NF.

As the title of that book might suggest, these developments turn out to be particularly important in connection with temporal data, and they’re discussed in detail in that book. However, temporal data as such is beyond the scope of the book you’re reading right now; all I want to do here is give a definition of 6NF that works for “regular”—i.e., nontemporal—data (and I’ll assume from this point forward that all data is “regular” in this sense). Appealing only to projection and join as classically defined, therefore (and hence only to JDs as classically defined also),^{[122]} here’s the 6NF definition:

**Definition:**Relvar*R*is in**sixth normal form**(6NF) if and only if the only JDs that hold in*R*are trivial ones. In other words, the only JDs that hold in*R*are of the form {...,*H*,...}, where*H*is the heading.

Of course, we can never get rid of trivial dependencies; thus, a relvar ...

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