Partially Ordered Sets
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The present chapter gives some mathematical theory of partially ordered sets. Referring to the appendix on terminology, we recall that a partially ordered set is a pair (X, ≺) where ≺ is an irreflexive and transitive relation on X. We shall not immediately give the interpretation of the elements of X. For the purpose of this chapter, it suffices to think of a poset (X, ≺) as describing a history or a process (of a concurrent system) and of an element x ∊ X as representing a basic occurrence, i.e., an item which has occurred once, and only once, in the history given by (X, ≺). The relation ≺ means ‘before’; that is, x ≺ y means that x has occurred earlier than y in the history given by (X, ≺).
KeywordsInduction Hypothesis World Line Graphical Notation Finite Degree Infinite Line
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