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However, in general, the two-element set {true, false} must be replaced by an object Ω with more than two truth-values, though a distinguished arrow into Ω is still labeled as true.
It suffices to define this as the two-element set {0, 1}, the constants (zeroary operations) 0 and 1, and the 2²² = 16 binary operations.
The range of the characteristic function of a classical set X is the two-element set {0,1} (which may be seen as the set of classical truth values).
So, in doubly directed partial orders, each two-element set is contained in at least one order interval, and we define ([a,c,b]_D) to mean that (c) is contained within each order interval also containing (a) and (b).
While it is true that (_O) is first-order definable from (_P,) the opposite is not the case: both a total ordering and an antichain ordering i.e., no two elements are comparable on a two-element set give rise to the same interpretation for (_O,) but not for (_P).
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Completeness Does the element set completely describe the objects?
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The pos-list of each component is simply the set of positions (1st element of the quadruples) under it.
If I consider off-maindiagonal non-zero elements in upper triangle of hines matrix, do they form a maximal set ?
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