Ted Cruz’s mom is an American citizen so he is an American citizen.
I was reading that our Framers never really defined “natural-born citizen.”
Cruz is naturalized by 8 U.S.C. § 1401(g)
Of course, no one disagrees with the statement that Cruz is an American citizen. And he may have been an American citizen at birth, depending on what the statute was at the time of his birth.
But, as I said, "Natural Born Citizen(s)" is(are) a subset of "citizen(s) at birth."
I was reading that our Framers never really defined “natural-born citizen.”
They never formally defined "Natural Born Citizen" because the definition was well understood among the erudite of their time and place. The term had been defined by the Swiss political commentator Vattel about thirty years prior to the creation of the Constitution, and the Framers had read Vattel (most could read French) or knew from their contemporaries what Vattel meant by "Natural Born Citizen": a person born in a particular nation both of whose parents were citizens of that nation at the time of that person's birth.
During the Constitutional Convention, John Jay (who was not present and who was so distinguished a lawyer that he would become the first Chief Justice of the Supreme Court) sent a letter to George Washington (who presided over the Convention), recommending the requirement that the President be a "Natural Born Citizen." Washington didn't have to ask Jay or anyone else what Jay meant in his letter. He and the others present all knew very well what "Natural Born Citizen" meant.
Any attempt to suggest otherwise is revisionist history, calculated to change the meaning of the Constitution so as to falsely create presidential (or vice-presidential) constitutional eligibility for current people whom one might favor but who do not meet the Natural Born Citizen requirement.