The multiverse-of-sets tag has no wiki summary.

**5**

votes

**2**answers

535 views

### Is the Mostowski collapse natural?

The Mostowski collapse lemma (see here for a quick ref) is one of the key basic tools in the set-theory arsenal. I wonder if the collapse is natural, in the functorial sense.
More precisely, is ...

**42**

votes

**3**answers

2k views

### Forcing as a new chapter of Galois Theory

There is a (very) long essay by Grothendieck with the ominous title La Longue Marche à travers la théorie de Galois (The Long March through Galois Theory). As usual, Grothendieck knew what he was ...

**9**

votes

**1**answer

1k views

### Set-theoretical multiverse and foundations

I just had a look to the article The set theoretical multiverse by (mo user) J.D.Hamkins. Not being a logician and not knowing forcing techniques, I couldn't fully appreciate the mathematical ideas, ...

**6**

votes

**0**answers

304 views

### Maps between forcing posets

We all know that forcing can be seen (if you like things that way) as a category of sheaves over the poset of forcing conditions equipped with the double negation Grothendieck topology. As such it is ...

**29**

votes

**3**answers

2k views

### The set-theoretic multiverse as a (bi)category

Joel Hamkin's The set-theoretic multiverse has featured in MO questions before, e.g., here and here. But I was wondering about the best category theoretic angle to take on it.
In the paper Joel ...