original passage: A real number "a" is first-order definable in the language of set theory, without parameters, if there is a formula "φ" in the language of set theory, with one free variable, such that "a" is the unique real number such that "φ"("a") holds (see). This notion cannot be expressed as a formula in the language of set theory.
original sentence: This notion cannot be expressed as a formula in the language of set theory.
sentence2: Does the passage make it sound like a mathematical discovery that came after set theory, or that is more complex than set theory, is necessary to express this notion?
sentence1: A real number "a" is first-order definable in the language of set theory, without parameters, if there is a formula "φ" in the language of set theory, with one free variable, such that "a" is the unique real number such that "φ"("a") holds (see). This notion cannot be expressed as a formula using simple mathematics, and so it required the creation of the language of set theory to be formally expressed.