Haim Gaifman’s first result (obtained when he was a math student) was the equivalence of context-free grammars and categorial grammars. He was Carnap’s research assistant, working on the foundations of probability theory, and got his PhD under Tarski (on infinite Boolean algebras). He worked on a broad spectrum of subjects: in mathematical logic (mostly set theory, where he invented the technique of iterated  ultrapowers, and models of Peano’s arithmetic), foundations of probability (where he defined probabilities on first-order and on richer languages), in philosophy of language and  philosophy of mathematics, as well as in theoretical computer science.

He held various permanent and visiting positions in mathematics, philosophy and computer science departments. He is Professor Emeritus of Mathematics and Eleanor Roosevelt Professor in History and Philosophy of Science at Hebrew University. While he was professor of mathematics at the Hebrew University, he taught courses in Philosophy and  directed the program in History and Philosophy of Science.

His recent interests include foundations of probability, rational choice, philosophy of mathematics, logical systems that formalize aspects of natural reasoning,  Frege, Russell and theories of naming.