Series: Penn State Logic Seminar

Date: Tuesday, October 5, 2004

Time: 2:30 - 3:45 PM

Place: 307 Boucke Building


  Dana S. Scott, Carnegie Mellon University, 
  Mathematics - Philosophy - Computer Science


  The Algebraic Interpretation of Classical and Intuitionistic


  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.