Let $\leq_t$ be a total order relation over a set X.
I want to define "the" strict linear order relation $<_t$ associated with $\leq_t$. Firstly , is there a name for such a associated relation ?
Secondly , what's the best description (or a good description that does not permit counter example or non sense) for it ?
I would write that , < needs to be transitive , trichotomous , and that for each $x ,y\in X$,$x<_t y\Rightarrow x\leq_t y$ , but i'm not sure it's a good description.