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The possible states of different objects defined in this way can be conceived as representing potential events. The set of events can then be structured in the same way as invariance of causal structure, or local-to-global causal connections or even formal properties of global causal connections.
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According to, "A minimal realization of such a relationally determined space-time structure can be found". In this model there are, however, no explicit distinctions. This is equivalent to a model where each object is characterized by only one distinction: (presence, absence) or (existence,
193:, etc.), the set of true propositions will not be inconsistent but will correspond to a particular maximal conjunction of propositions, denoting the (atomic) state. (The true propositions form an ultrafilter, the false propositions form a maximal ideal, as mentioned above.)
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If more than one distinction is considered, however, the model becomes much more complex, and the interpretation of distinction states as events, or morphisms as processes, is much less straightforward.
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non-existence) of an event. In this manner, "the 'arrows' or the 'structural language' can then be interpreted as morphisms which conserve this unique distinction".
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The morphisms between (non-trivial) objects could be viewed as representing causal connections leading from one event to another one. For example, the morphism
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which are mapped to 1 are true, and the propositions mapped to 0 are false. Since the morphism conserves the
Boolean operators (
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can be interpreted as representing a particular "state of that object", namely the one where the propositions of
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2-valued morphisms have also been proposed as a tool for unifying the language of physics.
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or chronological precedence relations. These relations would then determine a temporal
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Fleischer, Isidore (1993), "A Boolean formalization of predicate calculus",
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are viewed as "propositions about some object", then a 2-valued morphism on
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that sends the ultrafilter to 1 and the maximal ideal to 0.
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that sends the ultrafilter to 1 and the maximal ideal to 0.
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A Structural
Language for the Foundations of Physics
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is a 2-valued morphism, then the set of elements of
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2-valued morphisms, ultrafilters and maximal ideals
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