Series: Penn State Logic Seminar Date: Tuesday, October 5, 2004 Time: 2:30 - 3:45 PM Place: 307 Boucke Building Speaker: Dana S. Scott, Carnegie Mellon University, Mathematics - Philosophy - Computer Science Title: The Algebraic Interpretation of Classical and Intuitionistic Quantifiers Abstract: In their 1963 book, "The Mathematics of Metamathematics", Rasiowa and Sikorski present an approach to completeness theorems of various logics using algebraic methods. This idea can of course be traced back to Boole, but it was revived and generalized by Stone and Tarski in the 1930s; however, the most direct influence on their work came from their well-known colleague, Andrzej Mostowski, after WW II. Mostowski's interpretation of quantification can as well be given for intutionistic as classical logic. The talk will briefly review the history and content of these ideas and raise the question of why there was at that time no generalization made to higher-order logic and set theory. Entirely new light on this kind of algebraic semantics has more recently been thrown by the development of topos theory in category theory. Reasons for pursuing this generalization will also be discussed.