"I'm Jim", "So am I"

Some years ago, 2 identical twins were born in Minnesota USA. They were adopted by 2 different families. The 2 new families both called their babies Jim. Jim Springer never knew that Jim Lewis existed. But when they were 40 years old they met for the first time and they had a conversation something like this..

"Hi! I'm Jim."
"So am I. Great to meet you. Are you married, Jim?"
"Yes.. well, I've been married twice."
"Yeah? So have I. Do you have any children?"
"I have one son."
"So do I. What's his name?"
"James."
"That's amazing! My son's name is James too."
"Did you go to university, Jim?"
"No, I didn't."
"Neither did I. I was a terrible student."
"So was I. What do you like doing in your free time, Jim?"
"I like making things, especially with wood."
"That's incredible! So do I."
"But I don't do any exercise at all. Look at me."
"Don't worry. Neither do I."
"Do you smoke?"
"Yes. I smoke Salem cigarettes."
"So do I! What car do you have?"
"A Chevrolet."
"Me too! Let's go and have a drink. What beer do you drink?"
"Miller Lite."
"So do I!"