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A transitive antisymmetric relation among the elements of a set, which does not necessarily apply to each pair of elements.
‘Viewed another way, what this says is that if we define a partial ordering on strings such that one string is greater than another if it contains the second as a substring, then there is no infinite antichain.’
‘Shoham's theory is based on a partial order over models: S can then be characterized as the set of models in K that are minimal in K.’
‘An attempt to articulate a range of scenarios in which partial ordering of secondary and tertiary structures mutually enhance a favorable folding pathway has been presented under the label of ‘nucleation-condensation’.’
‘In fact, it can be shown that the possible ancestral combinations of adjacent copies are given by the maximal antichains of the partial order on the duplication events.’
‘In terms of sets, a partial ordering can be obtained by using set inclusion, the relation ‘is a subset of,’ where subset also includes the meaning that a set is a subset of itself.’