Combinatorics of the reals and independence results - talk by Diana Carolina Montoya

Description

Dr. Diana Carolina Montoya, a PostDoc at University of Vienna, gave a talk at our Institute. Abstract: In this talk, I will give an introduction to the area of set theory known as infinitary combinatorics of the reals. The focus will consist on the study of particular subsets of the real line and the consequences that some axioms of set theory may have on their possible sizes. We will start from the very beginning, i.e. the continuum hypothesis and how the fact that this is an independent statement of the classical set theory axiomatic ZFC affects the combinatorics of the reals. After, we will focus on models in which the failure of ZFC fails and into introducing some cardinal characteristics associated to measure and category on the reals. In the end, I will talk about some results and techniques that modern set theory uses, as well as some open questions on this subject. I will give an introduction to some computability analogs of these cardinals to finish the talk with some inspiration on some applied lines of research.

Period	30 Mar 2023
Event type	Guest talk
Location	AustriaShow on map