How many sizes of infinity are there?

“O God, I could be bound in a nutshell, and count myself a king of infinite space – were it not that I have bad dreams.”

Hamlet, Act 2, Scene 2. Lines 252-254.

Recently, a colleague asked me:

I know that there are different sizes of infinity, but what I want to know is how many different sizes of infinity there are?

-Curious Colleague

This is a great question! I tried to explain my answer at the time, but it came out garbled and I think I confused him more than I helped. So this post is an effort to remedy that and answer his question.

Continue reading How many sizes of infinity are there?

Future of Set Theory – Panel Discussion

The following is a (somewhat complete) transcription of a panel discussion held at the Fields Institute on April 1, 2015 as part of the “Forcing and its Applications Retrospective” workshop.

The speakers were

  • Stevo Todorcevic (University of Toronto)
  • Jindrich Zapletal (University of Florida)
  • Christina Brech (University of São Paulo)
  • Assaf Rinot (Bar-Ilan University)
  • Matteo Viale (University of Torino)
  • Justin Moore (Cornell University, Moderator)

I took notes, so please bear in mind that some of this is paraphrased. I apologize if I misrepresented anyone, and I am happy to make corrections if I am emailed.

Continue reading Future of Set Theory – Panel Discussion