# Andrej Bauer: When there are countably many reals

Date of publication: 19. 3. 2024

Mathematics and theoretical computing seminar

Thursday

21

March

Time:

10:00 - 12:00

Location:

Jadranska 21, 3.07

**Abstract:** We shall take a closer look at the parametric realizability topos in which the Dedekind reals form a countable set. The topos exhibits other strange properties. For example, the Hilbert cube is countable as well, all maps are continuous, Brouwer's fixed point theorem holds, the closed interval has outer measure 0, it can be covered by an open cover without a finite subcover, but every countable cover by rational intervals has a finite subcover.

This is joint work with James Hanson.