### 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

- Axiom of determinacyImplications of the axiom of determinacy ← Older revision Revision as of 20:59, 18 October 2017 (3 intermediate revisions by the same user not shown)Line 51: Line 51: ** The [[club]] filter on $\omega_1$ is an ultrafilter. ** The [[club]] filter on $\omega_1$ is an ultrafilter. ** The club filter on $\omega_2$ restrained to sets of […]Wabb2t
- ReflectingAdded small remark of $\aleph$-fixed point-ness ← Older revision Revision as of 03:56, 13 October 2017 Line 13: Line 13: * A simple Löwenheim-Skolem argument shows that every infinite cardinal $\kappa$ is $\Sigma_1$-correct. * A simple Löwenheim-Skolem argument shows that every infinite cardinal $\kappa$ is $\Sigma_1$-correct. * For each natural number $n$, the $\Sigma_n$-correct cardinals form […]Zetapology
- BethBeth fixed point ← Older revision Revision as of 18:20, 12 October 2017 Line 26: Line 26: == Beth fixed point == == Beth fixed point == −A cardinal $\kappa$ is a ''$\beth$-fixed point'' when $\kappa=\beth_\kappa$. Just as in the construction of [[aleph fixed point | aleph fixed points]], we may similar construct beth fixed […]Wabb2t
- BethEvery $\beth$-fixed point is an $\aleph$-fixed point ← Older revision Revision as of 17:02, 12 October 2017 Line 26: Line 26: == Beth fixed point == == Beth fixed point == −A cardinal $\kappa$ is a ''$\beth$-fixed point'' when $\kappa=\beth_\kappa$. Just as in the construction of [[aleph fixed point | aleph fixed points]], we may […]Zetapology
- User blog:Zetapology/Inexplicable cardinalsFixed definition ← Older revision Revision as of 14:42, 12 October 2017 Line 24: Line 24: === $n$-Inexplicable cardinals=== === $n$-Inexplicable cardinals=== −Let an initial ordinal (i.e. a cardinal assuming AC) $\kappa$ be '''$n$-Inexplicable''' when $\theta_\kappa(n)=\kappa$. This is equivalent to $\exists\alpha(\theta_\alpha(n)=\kappa)$. Each of these are $\aleph$-fixed points, and fixed points of the enumerations of those, […]Zetapology

- Axiom of determinacy

# 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.