  We present a formalization of collections that Cornelius Castoriadis calls
``magmas'', especially the property which mainly characterizes them and
distinguishes them from the usual cantorian sets. It is the property of their
elements to {\em depend} on other elements, either in a one-way or a two-way
manner, so that one cannot occur in a collection without the occurrence of
those dependent on it. Such a dependence relation can be represented by a
pre-order relation $\preccurlyeq$ Then, working in a mild strengthening of the
theory ${\rm ZFA}$, where $A$ is an infinite set of atoms equipped with a
primitive pre-ordering $\preccurlyeq$, the class of magmas over $A$ is
represented by the class $LO(A,\preccurlyeq)$ of nonempty open subsets of $A$
with respect to the lower topology of $\langle A,\preccurlyeq\rangle$. Next the
pre-ordering $\preccurlyeq$ is shifted (by a kind of simulation) to a
pre-ordering $\preccurlyeq^+$ on ${\cal P}(A)$, which turns out to satisfy the
same non-minimality condition as well, and which, happily, when restricted to
$LO(A,\preccurlyeq)$ coincides with $\subseteq$. This allows us to define a
hierarchy $M_\alpha(A)$, along all ordinals $\alpha\geq 1$, the``magmatic
hierarchy'', such that $M_1(A)=LO(A,\preccurlyeq)$,
$M_{\alpha+1}(A)=LO(M_\alpha(A),\subseteq)$, and
$M_\alpha(A)=\bigcup_{\beta<\alpha}M_\beta(A)$, for a limit ordinal $\alpha$.
For every $\alpha\geq 1$, $M_\alpha(A)\subseteq V_\alpha(A)$, where
$V_\alpha(A)$ are the levels of the universe $V(A)$ of ${\rm ZFA}$. The class
$M(A)=\bigcup_{\alpha\geq 1}M_\alpha(A)$ is the ``magmatic universe above
$A$.''
