Löwenheim-Skolem Song

            One way makes it larger
            and the other makes it small
            If you want to find a model
            Of any size at all
            Go ask L-S
            Leopold and Thoralf


            If you have two nested structures
            Then to show that they agree
            On each first-order sentence
            You could ask conceivably
            Just find a witness
            For every backwards E


            To make this happen, add a function
            For every existential
            If there's a witness, just point to one
            If not, then return null
            There's a substructure
            Of size omega plus L


            If logic and proportion
            Have fallen to their knees
            When we add some distinct constants
            and every sentence about these
            The contradiction was with us already
            Compactly, QED