M.Sc. in Hebrew, Jerusalem (1958)
Ph.D., U.C. Berkeley, in mathematics under Tarski, (1962).
Professor Gaifman's first result was about context-free grammars, after which he worked on the foundations of probability theory (with Carnap), and got his Ph. D. under Tarski (on infinite Boolean algebras). He worked on a broad spectrum in mathematical logic (mostly set theory and models of Peano's arithmetic), foundations of probability, as well as theoretical computer science and philosophy. He held various permanent and visiting positions in mathematics, computer science and philosophy departments. Before coming to Columbia, in 1990 he was professor of mathematics at the Hebrew University; at the same time he taught courses in philosophy and, for several years, directed the program in History and Philosophy of science.
Gaifman's recent interests include logical systems that formalize aspects of natural reasoning, (pointer logic for solving the semantic paradoxes, contextual logic for handling vagueness and the Sorites paradox), phenomena of self-reference, philosophy of language, metaphysical realism, philosophy of logic, philosophy of mathematics, Frege, Russell, the early Wittgenstein, and foundations of probability. His recent works include ``Non-Standard Models in a Broader Perspective'' (in the 2003 AMS collection Nonstandard Models of Arithmetic and Set Theory, edited by A. Enayat and R. Kossak), “Reasoning with Limited Resources and Assigning Probabilities to Arithmetical Statements'' (to appear in Synthese), ``Some Thoughts and a Proposal in the Philosophy of Mathematics'' (to appear in the proceedings of the 2003 International Congress in Logic Methodology and Philosophy of Science), and manuscripts in preparation: “Fixed point theorems in a general setting” and “Russellian Substitutional Algebras”
Logic; Probability Theory; Philosophy of Language