Jim, Arnold isn't running because he's a naturalized citizen of the United States, not a natural-born citizen. He was born an Austrian citizen and went through a legal process to become a U.S. citizen. Madeleine Albrght also cannot run for President because she also is a naturalized citizen. She was born a citizen of Czechoslavakia. But even if Obama had been born in Kenya, as I mistakenly thought he had been, he would still be a natural-born citizen of the U.S. because his mother was a U.S. citizen.   

The law or the United States regarding birth-right citizenship, also known as natural-born citizenship, is this:

1) Any person born on U.S. territory is automatically a citizen of the Unitied States, regardless of the citizenship status of his parents. The only notable exception to this rule is that the children of foreign diplomats or occupying forces are not automatically U.S. citizens.

2) Any person whose mother is a citizen of the United States is automatically a U.S. citizen regardless of whether or not the birth takes place on U.S. soil. It makes no difference whether or not the father is a U.S. citizen.

3) Any person whose father is a U.S. citizen, but whose mother is not, is automatically a U.S. citizen, provided that the father acknowledges paternity by the child's 18th birthday.

Any natural-born citizen can run for President, regardless of where he was born, regardless of where he grew up, as long as he's at least 35 years old and has lived in the U.S. for fourteen years.