Manuscript En08-A@1 · En08-A.tex · proposition · c688d76d

Proposition: Nonuniqueness of chronology

Chronology, horismos, and operational sharpness › A causal order does not specify chronology · lines 1060–1075 · proof included or linked

En08-A@1#prop:chronnonunique

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Every partial order admits both

I = \emptyset and I = J ∖ {(x, x) : x \in E}

with these properties.

Proof. The empty case is immediate. For strict order, if $x \leq y < z$ , then $x \leq z$ . Equality $x = z$ would contradict antisymmetry, so $x < z$ . The other push-up implication is analogous.

Displayed formulas in this passage

unlabeled · line 1063
$I = \emptyset and I = J ∖ {(x, x) : x \in E}$

Nearby in this section

section: A causal order does not specify chronology
definition: Definition: Causal-space properties used here
section: A causal order does not specify chronology