  To continue the example of the field R of real numbers: It is often not at all obvious whether two given structures are or are not elementarily equivalent. One of the greatest achievements of the pre-history of model theory was Tarski’s description in 1930 of Th(R) (which he published in full only after the war; see his book in the Bibliography below). This description implied among other things that the structures elementarily equivalent to R are exactly the real-closed fields, a class of fields which was already known to the algebraists in its own right.