Countable unions of countable sets, their power sets, and the axiom of choice

Date

04/11/2019

Horaire

15:15 à 16:15

Diffusion

Résume

The union of countably many countable sets is countable, assuming the axiom of choice, and its power set is finite or the same size as the real numbers. But what happens without the axiom of choice? We will go over the basic results and slowly builds towards the theorem of D.B. Morris: There is no bound on how many subsets a countable union of countable sets can have.

(Only rudimentary knowledge in set theory is needed.)