Even though set theory purports to offer a foundation for all of mathematical practice, it would seem very odd to hear someone say, say, "I work in a narrow branch of set theory called partial differential equations."

My question: how would a set theory expert in 2011 characterize the scope, or purview, or principal goals of his or her subject? I have particular interest in aspects of the answer that might differ from what an expert might have said perhaps 20 years ago.