### Recent Writing

- 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
- Computable processes which produce any desired output in the right nonstandard model
- Virtual large cardinals
- Virtual Set Theory and Generic Vopěnka’s Principle

### 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

- BerkeleyAdded that the critical point of j can be arbitrary large above kappa. Removing this notion results in a "Proto-Berkeley" cardinal. Source: http://logic.harvard.edu/blog/wp-content/uploads/2014/11/Deep_Inconsistency.pdf ← Older revision Revision as of 14:40, 23 June 2017 Line 1: Line 1: −A cardinal $\kappa$ is a ''Berkeley'' cardinal, if for any transitive set $M$ with $\kappa\in M$, there is […]Dan Saattrup Nielsen

- Berkeley

# Category Archives: talks

## 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.

## Virtual large cardinals

This is a talk at Set Theory Day in New York, March 11, 2016.

Posted in talks
Tagged $\alpha$-iterable cardinals, forcing, large cardinals, remarkable cardinals, virtual large cardinals
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## Ehrenfeucht principles in set theory

This is a talk at the British Logic Colloquium in Cambridge, UK, September 2-4, 2015.