### 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

- SupercompactProper forcing axiom ← Older revision Revision as of 22:12, 18 November 2017 (One intermediate revision by the same user not shown)Line 42: Line 42: === Proper forcing axiom === === Proper forcing axiom === −Baumgartner proved that if there is a supercompact cardinal, then the proper forcing axiom holds in a forcing extenion. PFA's […]Julian Barathieu
- PFARedirected page to Forcing#Proper forcing ← Older revision Revision as of 22:10, 18 November 2017 Line 1: Line 1: −#REDIRECT [[Forcing]]+#REDIRECT [[Forcing#Proper forcing]]Julian Barathieu
- Forcing← Older revision Revision as of 21:55, 18 November 2017 (4 intermediate revisions by the same user not shown)Line 58: Line 58: === Separativity === === Separativity === −A forcing notion $(\mathbb{P},\leq)$ is ''separative'' if for all $p,q\in\mathbb{P}$, if $p\not\leq q$ then there exists a $r\leq p$ incompatible with $q$. Many notions aren't separative, for […]Julian Barathieu
- Upper attic← Older revision Revision as of 21:10, 18 November 2017 (One intermediate revision by the same user not shown)Line 19: Line 19: * [[nearly supercompact]] and [[nearly supercompact#Nearly strongly compact | nearly strongly compact]] cardinals * [[nearly supercompact]] and [[nearly supercompact#Nearly strongly compact | nearly strongly compact]] cardinals * [[Weakly_compact#Indestructibility of a weakly compact cardinal|indestructible weakly […]Julian Barathieu
- Proper Forcing AxiomRedirected page to Forcing#Proper forcing New page#REDIRECT [[Forcing#Proper forcing]]Julian Barathieu

- Supercompact

# Author Archives: Victoria Gitman

## 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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## The exact strength of the class forcing theorem

V. Gitman, J. D. Hamkins, P. Holy, P. Schlicht, and K. Williams, “The exact strength of the class forcing theorem.” (Submitted) PDF Citation arχiv @ARTICLE{GitmanHamkinsHolySchlichtWilliams:ForcingTheorem, AUTHOR= {Victoria Gitman and Joel David Hamkins and Peter Holy and Philipp Schlicht and … Continue reading

## A model of the generic Vopěnka principle in which the ordinals are not $\Delta_2$-Mahlo

V. Gitman and J. D. Hamkins, “A model of the generic vop\v enka principle in which the ordinals are not $\Delta_2$-mahlo.” (Submitted) PDF Citation arχiv @ARTICLE{GitmanHamkins:GVP, AUTHOR= {Victoria Gitman and Joel David Hamkins}, TITLE= {A model of the generic … Continue reading

## 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 large cardinals

V. Gitman and R. Schindler, “Virtual large cardinals.” (Submitted) PDF Citation @ARTICLE{GitmanSchindler:virtualCardinals, AUTHOR= {Gitman, Victoria and Schindler, Ralf}, TITLE= {Virtual large cardinals}, Note ={Submitted}, pdf={https://boolesrings.org/victoriagitman/files/2017/03/virtualLargeCardinals.pdf}, }

Posted in publications
Tagged R. Schindler, remarkable cardinals, virtual large cardinals
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## 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.

## The oddities of class forcing

I recently finished reading a series of excellent articles by Peter Holy, Regula Krapf, Philipp Lücke, Ana Njegomir and Philipp Schlicht investigating properties of class forcing over models of ${\rm GBC}$ (Gödel-Bernays set theory). So I would like to summarize … Continue reading