### 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

# Category Archives: talks

## 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
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## Filter games and Ramsey-like cardinals

This is a talk at the CUNY Set Theory Seminar, October 20, 2017.

Posted in talks
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## A model of second-order arithmetic with the choice scheme in which $\Pi^1_2$-dependent choice fails

This is a talk at the Kurt Gödel Research Center Research Seminar in Vienna, Austria, May 18, 2017.

## Computable processes which produce any desired output in the right nonstandard model

This is a talk at the special session “Computability Theory: Pushing the Boundaries” of 2017 AMS Eastern Sectional Meeting in New York, May 6-7.

## Virtual Set Theory and Generic Vopěnka’s Principle

This is a talk at the VCU MAMLS Conference in Richmond, Virginia, April 1, 2017.

## A countable ordinal definable set of reals without ordinal definable elements

This is a talk at the CUNY Set Theory Seminar, February 10, 2017.

## A set-theoretic approach to Scott’s Problem

This is a talk at the National University of Singapore Logic Seminar, October 19, 2016.

Posted in talks
Tagged Ehrenfeucht's lemma, PFA, proper families of reals, scott sets
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## Generic Vopěnka’s Principle at YST2016

This is a talk at the Young Set Theory 2016 Conference in Copenhagen, Denmark, June 13-17, 2016.

## Generic Vopěnka’s Principle

This is a talk at the Rutgers Logic Seminar in New Jersey, May 2, 2016.

## Computable processes can produce arbitrary outputs in nonstandard models

This is a talk at the CUNY MOPA Seminar in New York, April 13, 2016.