Abstract: In the proceedings of Logic Colloquium ’69, Georg Kreisel published a seminal paper on reasons for generalising recursion theory (now computability theory), and one purpose stressed by Kreisel was that such generalisations give us the opportunity to understand which properties of being finite are used in mathematical arguments.
In this non-technical talk we will survey parts of generalised computability theory with a focus on how various properties of finite sets were generalised in infinitary settings.
This talk is joint with the Oslo Logic Seminar. The talk will take place on Zoom. Contact Laura.Crosilla @ ifikk.uio.no for a Zoom-invite.