 If "F" has no constants, then "F" is extended by adding an arbitrary new constant.Let "L"σ be a first-order language with the vocabulary 
then the Herbrand universe of "L"σ (or σ) is {"c", "f"("c"), "g"("c"), "f"("f"("c")), "f"("g"("c")), "g"("f"("c")), "g"("g"("c")), ...}.Notice that the relation symbols are not relevant for a Herbrand universe.