Andres Villaveces
Mathematics Department
Ciudad Universitaria
Bogota, Colombia

"The expressive power of first order logic, and its weakness in mathematics"

ABSTRACT:

We address the issue of what we can expect logic to say on certain types of groups and classes of Banach spaces... and what we cannot expect logic to say.

The strength of classical theorems in model theory arises, somewhat paradoxically, from _limitations_ in the expressive power of first order logic. The compactness theorem, in principle the main cause of many of those limitations in expressive power, is in many cases the engine of many constructions and impressive classifications.

When we strengthen the expressive power we (almost always) lose the usual possibilities of using the constructions and theorems from FOL.

However, since a long while, several people have strengthened the logic, in order to capture more classes of structures of mathematical interest.

I will present in this talk _some_ of the issues mentioned, as well as some applications of ideas from non elementary classes to problems of universality in Banach spaces (due to Dzamonja and Shelah). I will also mention some of the most difficult issues with doing away with compactness.

This is a talk for wide mathematical public.
 

Back to Talks Page