### 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

- Constructible universeImplications, equivalences, and consequences of $0^\#$'s existence ← Older revision Revision as of 11:26, 14 December 2017 Line 63: Line 63: If $0^\#$ exists then: If $0^\#$ exists then: −* $\aleph_\omega$ is [[stable]] in $L$ and so $0^\#$ also corresponds to the set of the Gödel numberings of first-order formulas $\varphi$ such that $L\models\varphi(\aleph_0,\aleph_1...\aleph_n)$+* $L_{\aleph_\omega}\prec […]Julian Barathieu
- Axiom of determinacy← Older revision Revision as of 11:13, 14 December 2017 Line 100: Line 100: * Every uncountable cardinal $Julian Barathieu
- Upper attic← Older revision Revision as of 11:07, 14 December 2017 Line 30: Line 30: * [[zero dagger| $0^\dagger$]], $j:L[U]\to L[U]$ cardinal * [[zero dagger| $0^\dagger$]], $j:L[U]\to L[U]$ cardinal * '''[[measurable]]''' cardinal, [[weakly measurable]] cardinal, singular [[Jonsson|Jónsson]] cardinal * '''[[measurable]]''' cardinal, [[weakly measurable]] cardinal, singular [[Jonsson|Jónsson]] cardinal −* [[Jonsson | Jónsson]] cardinal, [[Rowbottom]] cardinal, '''[[Ramsey]]''' cardinal, [[strongly Ramsey]] […]Julian Barathieu
- Strongly compactDiverse characterizations ← Older revision Revision as of 08:57, 14 December 2017 Line 18: Line 18: A cardinal $\kappa$ is $\theta$-strongly compact if and only if there is an [[elementary embedding]] $j:V\to M$ of the set-theoretic universe $V$ into a transitive class $M$ with critical point $\kappa$, such that $j''\theta\subset s\in M$ for some […]Julian Barathieu
- 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

- Constructible universe

# Category Archives: publications

## 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

## 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}, }

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Tagged R. Schindler, remarkable cardinals, virtual large cardinals
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## Generic Vopěnka’s Principle, remarkable cardinals, and the weak Proper Forcing Axiom

J. Bagaria, V. Gitman, and R. Schindler, “Generic Vop\v enka’s Principle, remarkable cardinals, and the weak Proper Forcing Axiom,” Arch. math. logic, vol. 56, iss. 1-2, pp. 1-20, 2017. PDF Journal MR Citation @ARTICLE{BagariaGitmanSchindler:VopenkaPrinciple, AUTHOR = {Bagaria, Joan and … Continue reading

## Mitchell order for Ramsey and Ramsey-like cardinals

E. Carmody, V. Gitman, and M. Habič, “Mitchell order for Ramsey and Ramsey-like cardinals.” (Manuscript under review) PDF Citation @ARTICLE{CarmodyGitmanHabic:MitchellOrder, AUTHOR= {Carmody, Erin and Gitman, Victoria and Habi\v{c}, Miha}, TITLE= {Mitchell order for {R}amsey and {R}amsey-like cardinals}, Note ={Manuscript … Continue reading

## Open determinacy for class games

V. Gitman and J. D. Hamkins, “Open determinacy for class games,” in Foundations of mathematics, logic at harvard, essays in honor of hugh woodin’s 60th birthday, A. E. Caicedo, J. Cummings, P. Koellner, and P. Larson, Eds., American Mathematical Society, … Continue reading

## Ehrenfeucht’s lemma in set theory

G. Fuchs, V. Gitman, and J. D. Hamkins, “Ehrenfeucht’s lemma in set theory,” To appear in the notre dame journal of formal logic. PDF Citation arχiv @ARTICLE{fuchsgitmanhamkins:ehrenfeuchtLemma, AUTHOR= {Gunter Fuchs and Victoria Gitman and Joel David Hamkins}, TITLE= {Ehrenfeucht’s … Continue reading

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Tagged Algebraicity, Ehrenfeucht principles, Ehrenfeucht's lemma, G. Fuchs, J. D. Hamkins
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## Indestructibility properties of remarkable cardinals

Y. Cheng and V. Gitman, “Indestructibility properties of remarkable cardinals,” Arch. math. logic, vol. 54, iss. 7-8, pp. 961-984, 2015. PDF Journal MR Citation arχiv @ARTICLE{chenggitman:IndestructibleRemarkableCardinals, AUTHOR = {Cheng, Yong and Gitman, Victoria}, TITLE = {Indestructibility properties of remarkable … Continue reading

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Tagged forcing, indestructibility, remarkable cardinals, Yong Cheng
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## On ground model definability

V. Gitman and T. A. Johnstone, “On ground model definability,” in Infinity, computability, and metamathematics: festschrift in honour of the 60th birthdays of peter koepke and philip welch, London, GB: College publications, 2014. PDF Citation arχiv @INCOLLECTION{gitmanjohnstone:groundmodels, AUTHOR = … Continue reading