Hypothesis
27
[26H] We will study an order relation \(β€\) on \(β\) (not necessarily total) such that
\begin{align} β x ββ , & (0β€ x) \quad , \label{eq:caratt_ le_ N_ 0} \\ β x,y ββ , & (x{\lt} Sy) \iff (x β€ y ) \quad ; \label{eq:caratt_ le_ N} \end{align}
where as usual
\[ x{\lt}y β (xβ€ y)β§ (xβ y)\quad . \]