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Graphlet
In graph theory, a graphlet is an isomorphism class of a (typically small) connected graph. Graphlets are usually considered within the context of a large graph, where a graph may contain several isomorphic copies of a graphlet. In this way, graphlets are meant to capture the local topological properties of a graph.

Scott Isomorphism Theorem
In computability theory and infinitary logic, the Scott isomorphism theorem concerning infinitary descriptions of countable structures. The theorem states that every computable structure is determined up to isomorphism by an infinitary sentence called its Scott sentence. Notice this implies the Löwen-Skolem theorem fails for infinitary logics.

Statement of Barwise Compactness
Let $$A$$ be a countable admissible set. Let $$L$$ be an $$A$$-finite relational language. Suppose $$\Gamma$$ is a set of $$L_A$$-sentences, where $$\Gamma$$ is a $$\Sigma_1$$ set with parameters from $$A$$, and every $$A$$-finite subset of $$\Gamma$$ is satisfiable. Then $$\Gamma$$ is satisfiable. This is taken from Julia Knight's lecture notes for her Fall 2012 Topics course in Mathematical Logic.