Manuscript XXII-F@1 · XXII-F.tex · section · 67821705

The component order and matched equivalence

The component order and matched equivalence · lines 383–407

XXII-F@1#eq:influence, XXII-F@1#eq:quotient

On $E = N \times J$ , set

(e, a) R_{inf}_{D} (f, b) ⟺ e = f, a \neq = b, Δ_{e} (a, b) > 0.

There are no cross-identifier edges. Their absence describes the separately tested interface, not a measurement of an unspecified global causal relation.

Let $p ⇝_{D} q$ mean equality or finite directed reachability. Set

p \sim_{D} q ⟺ p ⇝_{D} q and q ⇝_{D} p, E_{D} = E / \sim_{D}, [p] ⪯_{D} [q] ⟺ p ⇝_{D} q .

Displayed formulas in this passage

XXII-F@1#eq:influence · line 386
$(e, a) R_{inf}_{D} (f, b) ⟺ e = f, a \neq = b, Δ_{e} (a, b) > 0.$
XXII-F@1#eq:quotient · line 398
$p \sim_{D} q ⟺ p ⇝_{D} q and q ⇝_{D} p, E_{D} = E / \sim_{D}, [p] ⪯_{D} [q] ⟺ p ⇝_{D} q .$

Nearby in this section

proposition: Proposition: Order and finite futures
section: The component order and matched equivalence
definition: Definition: Matched equivalence
lemma: Lemma: Order covariance
section: The component order and matched equivalence