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* is a set of events, not necessarily finite.
* is a family of finite subsets of , the subsets that are deemed to be consistent (not forbidden). If is one of these consistent sets, then every subset of must also be consistent. That is, must be closed under the operation of taking subsets.
* is a binary relation from consistent sets to elements of . The relation , for and is interpreted as meaning that when the events so far form set , this enables to be the next event. When , it is required

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