Series: Penn State Logic Seminar

Date: Wednesday, August 18, 2004

Time: 11:10 AM - 12:25 PM

Place: 312 Boucke Building

Speaker: Esteban Gomez-Riviere, Penn State, Mathematics

Title: Scott's Isomorphism Theorem  

Abstract:

   In first order logic, our formulas and sentences are finite strings
   created using the usual formulation rules.  We can extend these
   rules to create infinitely long sentences, though still with a
   finite number of free variables, to create infinitary logics which
   allow us to say much more about our structures.  We will look at
   the simplest such infinitary logic, which allows only countable
   strings, and, using some information from Ehrenfeucht-Fraisse
   games, we will prove Scott's Isomorphism Theorem.  Scott's theorem
   tells us that there is a sentence in this infinitary logic, called
   the Scott sentence, which allows us to define countable structures
   up to isomorphism.