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.