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

Definition: Generated affine cone representation

Reachability sums and affine cone representations › Discrete samples versus completed cone orders · lines 969–985

En08-A@1#def:affine, En08-A@1#eq:orderfaithful, En08-A@1#eq:generated

A generated affine cone representation of an event order is a triple $(ι, V, K)$ , where $ι : E \to V$ is injective, $K$ is proper, and

p \leq q K ⟺ ι (q) - ι (p) \in K, = cl cone {ι (q) - ι (p) : p < q} .

The existence of this data is the representation hypothesis $Aff$ . The corresponding completed order is the order on all of $V$ defined by differences in $K$ .

Displayed formulas in this passage

En08-A@1#eq:orderfaithful · line 974
$p \leq q K ⟺ ι (q) - ι (p) \in K, = cl cone {ι (q) - ι (p) : p < q} .$
En08-A@1#eq:generated · line 974
$p \leq q K ⟺ ι (q) - ι (p) \in K, = cl cone {ι (q) - ι (p) : p < q} .$

Nearby in this section

section: Discrete samples versus completed cone orders
proposition: Proposition: No continuum identification for a past-finite model
section: Discrete samples versus completed cone orders
proposition: Proposition: Finite increment obstruction
section: Discrete samples versus completed cone orders