### Recent Writing

- Virtual large cardinal principles
- Filter games and Ramsey-like cardinals
- The exact strength of the class forcing theorem
- A model of the generic Vopěnka principle in which the ordinals are not $\Delta_2$-Mahlo
- A model of second-order arithmetic with the choice scheme in which $\Pi^1_2$-dependent choice fails

### Mathoverflow Activity

- Comment by Victoria Gitman on Does Con(ZF + Reinhardt) really imply Con(ZFC + I0)?@Stefan For some reason, I cannot click on the link.Victoria Gitman
- Comment by Victoria Gitman on Cofinality of $j(\kappa)$ for a measurability embedding $j:V\to M$ with critical point $\kappa$@AsafKaragila I edited the question to make it clearer. Maybe I will ask your version as a follow-up if you don't ask it first :).Victoria Gitman
- Comment by Victoria Gitman on Cofinality of $j(\kappa)$ for a measurability embedding $j:V\to M$ with critical point $\kappa$@AsafKaragila I should have done a better job stating my question clearly. I wanted to know precisely what Yair answered: whether there are models where $\text{cf}(j(\kappa))$ is smaller than the size of $j(\kappa)$. Your interpretation of the question is very interesting as well, but I think much harder to answer.Victoria Gitman

- Comment by Victoria Gitman on Does Con(ZF + Reinhardt) really imply Con(ZFC + I0)?
### Cantor’s Attic

- Supercompact← Older revision Revision as of 21:12, 11 December 2017 Line 10: Line 10: One can see the equivalence of the two formulations by first considering the ultrafilter $U$ arising from the [[seed]] $j''\theta$, so that $X\in U\iff j''\theta\in j(X)$. It is easy to check that $U$ is a normal fine measure on $\mathcal{P}_\kappa(\theta)$. Conversely, […]Julian Barathieu
- Second-order← Older revision Revision as of 21:02, 11 December 2017 Line 45: Line 45: == Models of $\text{MK}$ == == Models of $\text{MK}$ == −In consistency strength, $\text{MK}$ is stronger than [[ZFC|$\text{ZFC}$]] and weaker than the existence of an [[inaccessible]] cardinal. It directly implies the consistency of $\text{ZFC}$. However, if a cardinal $\kappa$ is inaccessible […]Julian Barathieu
- GBCRedirected page to Second-order New page#REDIRECT [[Second-order]]Julian Barathieu
- NBGRedirected page to Second-order New page#REDIRECT [[Second-order]]Julian Barathieu
- KMRedirected page to Second-order New page#REDIRECT [[Second-order]]Julian Barathieu

- Supercompact

# Monthly Archives: October 2017

## Virtual large cardinal principles

This is a talk at the Harvard Logic Colloquium, Cambridge, November 8, 2017.

Posted in talks
Tagged forcing, Generic Vopěnka’s Principle, large cardinals, virtual large cardinals
2 Comments