### 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

- Community portal← Older revision Revision as of 20:21, 23 November 2017 (2 intermediate revisions by the same user not shown)Line 5: Line 5: This project aims to harness the abilities and efforts of the expert mathematical logic community---please help out! If you see a page that could be improved, please click to create an account, log […]Julian Barathieu
- ForcingOther examples of consistency results proved using forcing ← Older revision Revision as of 13:47, 23 November 2017 Line 115: Line 115: * Assume there is a supercompact cardinal. Then there is a generic extension in which there exists infinitely many cardinals $\delta$ above $2^{\aleph_0}$ such that both $\delta$ and $\delta^+$ have the tree property. […]Julian Barathieu
- Zero sharp← Older revision Revision as of 21:50, 22 November 2017 (2 intermediate revisions by the same user not shown)Line 1: Line 1: [[Category:Large cardinal axioms]] [[Category:Large cardinal axioms]] [[Category:Constructibility]] [[Category:Constructibility]] −$0^{\#}$ is a [[projective|$\Sigma_3^1$]] real number which cannot be proven to exist in [[ZFC|$\text{ZFC}$]]. It's existence contradicts the [[Axiom of constructibility]], $V=L$. In fact, it's existence is […]Julian Barathieu
- Zero sharpHopefully fixed for good ← Older revision Revision as of 20:34, 22 November 2017 (2 intermediate revisions by the same user not shown)Line 12: Line 12: "$0^{\#}$ exists" is used as a shorthand for "there is an uncountable set of Silver indiscernibles"; since $L_{\aleph_\omega}$ is a set, $\text{ZFC}$ can define a truth predicate for […]Zetapology
- Stable← Older revision Revision as of 17:39, 22 November 2017 (One intermediate revision by the same user not shown)Line 1: Line 1: [[Category:Lower attic]] [[Category:Lower attic]] [[Category:Reflection principles]] [[Category:Reflection principles]] − Stability was developed as a large countable ordinal property in order to try to generalize the different strengthened variants of [[admissible|admissibility]]. More specifically, they capture the […]Julian Barathieu

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# Monthly Archives: April 2012

## Models of $\rm{ZFC}^-$ that are not definable in their set forcing extensions

This is a talk at the CUNY Set Theory Seminar, May 4, 2012.