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The main theorem of this article is that every countable model of set theoryM, including every well-founded model, is isomorphic to a submodel of its ownconstructible universe. In other words, there is an embedding $j:M\to L^M$ thatis elementary for quantifier-free assertions. The proof uses universal digraphcombinatorics, including an acyclic version of the countable random digraph,which I call the countable random Q-graded digraph, and higher analoguesarising as uncountable Fraisse limits, leading to the hypnagogic digraph, aset-homogeneous, class-universal, surreal-numbers-graded acyclic class digraph,closely connected with the surreal numbers. The proof shows that $L^M$ containsa submodel that is a universal acyclic digraph of rank $Ord^M$. The method ofproof also establishes that the countable models of set theory are linearlypre-ordered by embeddability: for any two countable models of set theory, oneof them is isomorphic to a submodel of the other. Indeed, they arepre-well-ordered by embedability in order-type exactly $\omega_1+1$.Specifically, the countable well-founded models are ordered by embeddability inaccordance with the heights of their ordinals; every shorter model embeds intoevery taller model; every model of set theory $M$ is universal for allcountable well-founded binary relations of rank at most $Ord^M$; and everyill-founded model of set theory is universal for all countable acyclic binaryrelations. Finally, strengthening a classical theorem of Ressayre, the sameproof method shows that if $M$ is any nonstandard model of PA, then everycountable model of set theory---in particular, every model of ZFC---isisomorphic to a submodel of the hereditarily finite sets $HF^M$ of $M$. Indeed,$HF^M$ is universal for all countable acyclic binary relations.

Every countable model of set theory embeds into its own constructible universe