### 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

# Monthly Archives: January 2015

## 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

Posted in publications
Tagged Algebraicity, Ehrenfeucht principles, Ehrenfeucht's lemma, G. Fuchs, J. D. Hamkins
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