Graduate Students Seminar-An introduction to non-standard methods

Title: An introduction to non-standard methods

 

Abstract: Logicians have been able to create ``non-standard'' structures for over 100 years.  A non-standard structure is a structure that is ``similar'' to another, canonical structure, but different in key ways.  For example, in 1934, Thoralf Skolem constructed a structure which closely resembles ℕ, in that one can do all of arithmetic within the structure, but contains infinite, non-standard numbers.  Abraham Robonson developed the so-called hyperreal numbers, which are an extension of the regular real numbers, in which one can do calculus using infinitesimals.  In this talk, we will give a casual introduction to this type of construction, and, time permitting, discuss recent developments.