  If A is an L-structure, then we form the diagram of A as follows. First add to L a supply of new individual constants to serve as names for all the elements of A. (This illustrates how in first-order model theory we easily find ourselves using uncountable signatures. The ‘symbols’ in these signatures are abstract set-theoretic objects, not marks on a page.) Then using L and these new constants, the diagram of A is the set of all the atomic sentences and negations of atomic sentences that are true in A. 