Mariaclara Ragosta (Charles University) will give a talk on
An external perspective on internal objects
Abstract:
For any mathematical object X, one can consider a nonstandard extension *X, that is, roughly speaking, a more complicated object that somehow behaves in the same manner as X but that has a richer structure, namely *X is an elementary proper extension of X.
Also due to the strong connection with Ramsey Theory, it is particularly interesting to consider the set *N of hypernatural numbers and nonstandard extensions of related objects.
In this seminar we will focus on a typical nonstandard notion, namely internal objects, that are elements of some nonstandard extension *X. More specifically, we will deal with some special internal concepts that are particularly fascinating, and look at them from a perspective that is literally external.
We will explain that the name “internal” hides the philosophy for which, for one who lives within a nonstandard extension, internal elements are in some sense the only ones, while this is in fact false for one who has an external point of view. We will furthermore show the idea of some applications of this concept to recent advancements in Ramsey Theory.