Manuscript Oai283-A@1 · Oai283-A.tex · proposition · 6fb75895

Proposition: Finite-generation obstruction

Finite futures, three-relation typing, and cone obstructions › Faithful generation cannot be skipped · lines 1372–1388 · proof included or linked

Oai283-A@1#prop:finitecone

Back to manuscript

A finite event carrier cannot satisfy this generation rule with a cone linearly isomorphic to

L_{k} = {(t, x) \in R \times R^{k - 1} : t \geq ∥ x ∥_{2}}, k \geq 3.

Proof. A finite set of differences generates a polyhedral cone, which has only finitely many extreme rays. The Lorentz cone has an extreme ray $R_{\geq 0} (1, u)$ for every $u \in S^{k - 2}$ . Invertible linear maps preserve extreme rays.

Displayed formulas in this passage

unlabeled · line 1376
$L_{k} = {(t, x) \in R \times R^{k - 1} : t \geq ∥ x ∥_{2}}, k \geq 3.$

Nearby in this section

section: Faithful generation cannot be skipped
proposition: Proposition: Indistinguishable-trial symmetry obstruction
section: Faithful generation cannot be skipped