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

Sprache des Titels:

Englisch

Original Kurzfassung:

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.