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The structures $\langle M,\subseteq^M\rangle$ arising as the inclusionrelation of a countable model of sufficient set theory $\langleM,\in^M\rangle$, whether well-founded or not, are all isomorphic. Thesestructures $\langle M,\subseteq^M\rangle$ are exactly the countable saturatedmodels of the theory of set-theoretic mereology: an unbounded atomic relativelycomplemented distributive lattice. A very weak set theory suffices, even finiteset theory, provided that one excludes the $\omega$-standard models with noinfinite sets and the $\omega$-standard models of set theory with an amorphousset. Analogous results hold also for class theories such as G\"odel-Bernays settheory and Kelley-Morse set theory.

The inclusion relations of the countable models of set theory are all isomorphic