### 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

- Upper atticAdded n-fold Supercompact ← Older revision Revision as of 18:31, 22 October 2017 Line 7: Line 7: * '''[[Rank into rank]]''' cardinals $j:V_\lambda\to V_\lambda$, [[rank+1 into rank+1]] cardinal $j:V_{\lambda+1}\to V_{\lambda+1}$, I0 cardinal [[L of V_lambda+1 | $j:L(V_{\lambda+1})\to L(V_{\lambda+1})$]] * '''[[Rank into rank]]''' cardinals $j:V_\lambda\to V_\lambda$, [[rank+1 into rank+1]] cardinal $j:V_{\lambda+1}\to V_{\lambda+1}$, I0 cardinal [[L of V_lambda+1 […]Zetapology
- N-fold variantsAdded the page I guess New page{{DISPLAYTITLE: $n$-fold Variants of Large Cardinals}} = $n$-fold variants and $M^{(n)}$ = The $n$-fold variants of large cardinals were given in a very large paper by Sato Kentaro. Most of the definitions involve giving large closure properties to the $M$ used in the original large cardinal in an [[elementary […]Zetapology
- Upper atticchanged link ← Older revision Revision as of 05:31, 22 October 2017 (One intermediate revision by the same user not shown)Line 7: Line 7: * '''[[Rank into rank]]''' cardinals $j:V_\lambda\to V_\lambda$, [[rank+1 into rank+1]] cardinal $j:V_{\lambda+1}\to V_{\lambda+1}$, I0 cardinal [[L of V_lambda+1 | $j:L(V_{\lambda+1})\to L(V_{\lambda+1})$]] * '''[[Rank into rank]]''' cardinals $j:V_\lambda\to V_\lambda$, [[rank+1 into rank+1]] cardinal […]Zetapology
- SupercompactRelation to other large cardinals ← Older revision Revision as of 14:10, 21 October 2017 (One intermediate revision by the same user not shown)Line 11: Line 11: 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 […]Wabb2t
- FilterLarge cardinals ← Older revision Revision as of 12:54, 21 October 2017 Line 69: Line 69: If there exists a 2-valued $\kappa$-additive measure on $\kappa$, then $\kappa$ is a [[measurable]] cardinal. This equivalent to saying that there is a $\kappa$-complete nonprincipal ultrafilter on $\kappa$. If $j:V\to M$ is a nontrivial elementary embedding with critical point […]Wabb2t

- Upper attic

# Monthly Archives: September 2014

## 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

Posted in publications
Tagged forcing, indestructibility, remarkable cardinals, Yong Cheng
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