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In model theory, a model <math>\mathfrak{B}</math> is an extension of a model <math>\mathfrak{A}</math> (and <math>\mathfrak{A}</math> is a submodel of <math>\mathfrak{B}</math>) if and only if the universe A of <math>\mathfrak{A}</math> is a subset of the universe B of <math>\mathfrak{B}</math>, <math>\mathfrak{A}</math> and <math>\mathfrak{B}</math> share the same language <math>\mathcal{L}</math>, and the interpretations in <math>\mathfrak{A}</math> of the nonlogical symbols of <math>\mathcal{L}</math> are the restrictions to A of their interpretations in <math>\mathfrak{B}</math>.