Series: Penn State Logic Seminar

Date: Tuesday, April 23, 2002

Time: 2:30 - 3:45 PM

Place: 113 McAllister Building

Speaker: Deirdre Haskell, Mathematics, McMaster University

Title: Grothendieck Rings of Definable Sets


The collection of definable sets in a structure can be given a ring
structure in a natural way.  Sets are identified if there is a
bijection between them whose graph is a definable set.  The
Grothendieck group is the free group generated by the equivalence
classes, modulo the relation [X]+[Y]= [X cup Y] - [X cap Y].  The
multiplication [X].[Y]= [X times Y] gives the ring structure.  In this
talk I will give explicit calculations of the Grothendick rings of
various structures.