Definition
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[24X]Given \(x\) the successor is defined as
\begin{equation} S(x) {\stackrel{.}{=}}x ∪ \{ x\} \quad . \label{eq:successore} \end{equation}
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We will often write \(Sx\) instead \(S(x)\) to ease notations.
We say that a set \(A\) is S-saturated if \(∅∈ A\) and if for every \(x∈ A\) you have \(S(x)∈ A\). 1