Mathe im Beruf Detailseite

Speaker:
Giorgio Venturi (University of Pisa)

This talk will cover the paper, PER ASPERA AD ASTRA: FROM SKOLEM PARADOX TO AN UNCOUNTABLE UNIVERSE

Abstract

In this article we argue in favour of the existence of uncountable collections. Specifically, we will argue that the universe of set theory is uncountable. The argument is based on the analysis of Skolem Paradox and moves from its premises and from a comparison between Cantor Theorem and Cohen Theorem about the existence of generic filters. We then address an iterated version of the skeptic argument, outlining an important role that Hartogs Theorem can play in this respect. This paper also aims to connects the criticisms of the uncountable based on Skolem Paradox and the more recent discussion on Countabilism: the position according to which everything is countable.