# 2019 seminar talk: Spectrum of Independence

Talk held by Vera Fischer (KGRC) at the KGRC seminar on 2019-10-31.

### Abstract

We will consider some recent results concerning the spectrum of independence, i.e. the set of cardinalities of maximal independent families. In particular we will discuss the existence of models in which the spectrum is finite, models in which the spectrum is countably infinite and models in which the spectrum is arbitrarily large. If time permits, we will outline a proof of the consistency of $\mathfrak{i}<\mathfrak{a}_T$, which brings some light on the long-standing open question of the consistency of $\mathfrak{i}<\mathfrak{a}$.

Slides for this talk will appear here later.