In descriptive complexity theory we almost always suppose that there is a total order over the elements and that we can check equality between elements. This lets us consider elements as numbers: the element represents the number iff there are formula_3 elements with formula_4. Thanks to this we also may have the primitive predicate "bit", where formula_5 is true if only the th bit of the binary expansion of is 1. (We can replace addition and multiplication by ternary relations such that formula_6 is true iff formula_7 and formula_8 is true iff formula_9).