  We consider relations with no order on their attributes as in Database
Theory. An independent partition of the set of attributes S of a finite
relation R is any partition X of S such that the join of the projections of R
over the elements of X yields R. Identifying independent partitions has many
applications and corresponds conceptually to revealing orthogonality between
sets of dimensions in multidimensional point spaces. A subset of S is termed
self-correlated if there is a value of each of its attributes such that no
tuple of R contains all those values. This paper uncovers a connection between
independence and self-correlation, showing that the maximum independent
partition is the least fixed point of a certain inflationary transformer alpha
that operates on the finite lattice of partitions of S. alpha is defined via
the minimal self-correlated subsets of S. We use some additional properties of
alpha to show the said fixed point is still the limit of the standard
approximation sequence, just as in Kleene's well-known fixed point theorem for
continuous functions.
