Скачать с ютуб Proving Results Using the Structure of Mathematics - Yannis Wells в хорошем качестве

Proving Results Using the Structure of Mathematics - Yannis Wells

First-order logic and model theory give us a way to study the mathematical systems that we use in a rigorous manner, including how we are limited in what we can describe, and how truth relates to proof. One frequently overlooked application by those first experiencing the subject is how restrictions in what we can describe allow us to prove theorems entirely contained within a particular area of mathematics. This talk aims to give a brief introduction to the notion of formal logic and axiomatizations, and give two examples of how restrictions in what we can do allow us to prove concrete statements in graph theory and algebra, specifically Hall's Theorem in the case of infinite graphs and the Ax-Grothendieck Theorem. Viewers are expected to be familiar with the notion of a graph, a field, and have some knowledge of finite fields. Knowledge about first-order logic will be useful, but relevant content will be covered. -------------------------------------------------------------------------------- Subscribe:    / @thearchimedeans7041   Our website: https://archim.soc.srcf.net/ Our Facebook page:   / archimedeans   Join our mailing list: https://lists.cam.ac.uk/mailman/listi...