\relation{\longrightarrow}_{}
^{\varphi}  a,$$ where $\phi \in  \Phi_{0} \subset \Phi $, and for any $\phi \in \Phi_{0} $ there is no $x:1 \to a $ such that $\phi = x \circ !$. Here $ !:R_{T} \to 1 $ and $R_{+}$ is the subobject of object $R_{T}$ consisting of those $t$ for which $0 \le t $ (see definition of order in $R_{T}$ in [@St]).

An order $ \O $ is called [*conic*]{} if 1) for every $ y \in  p_{x} $ there exists a ray $ \lambda \subset p_{x}$ such that $ x, y \in \lambda $, and 2) $x$ is the origin of $\lambda$, i.e. if $ \mu $ is a ray and $ y \in \mu \subset \lambda $, $ \mu \neq \lambda $, then $x \notin \mu $.

An order $\O$ has [*the acute vertex*]{} or [*pointed*]{} one if for each $p_{x}$ there does not exist $\phi _{x} \in \Phi_{0} $ such that $\phi _{x} \subset p_{x}$. An order $\O$ is [*complete*]{}, if for any element $ z:1 \to  a$ and $p_{x}$ there exist different elements $ u_{x},v_{x}:1\to a $ and $   \phi \in \Phi_{0} $ such that $ z,u_{x},v_{x} \in  \phi $ and $ u_{x},v_{x} \in p_{x} 