### 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

- UltrapowerUltrapower axiom ← Older revision Revision as of 21:30, 19 November 2017 (2 intermediate revisions by the same user not shown)Line 49: Line 49: The ultrapower axiom ($\text{UA}$) has many significant consequences. Assume there is a [[strongly compact]] cardinal, then according to [https://arxiv.org/pdf/1710.03586.pdf]: The ultrapower axiom ($\text{UA}$) has many significant consequences. Assume there is a […]Julian Barathieu
- ForcingOther examples of consistency results proved using forcing ← Older revision Revision as of 19:31, 19 November 2017 Line 100: Line 100: Some other applications of forcing: Some other applications of forcing: −* There is a generic extension in which there is a cardinal $\kappa$ such that $2^{\mathrm{cf}(\kappa)}Julian Barathieu
- Supercompact← Older revision Revision as of 13:02, 19 November 2017 Line 6: Line 6: Generalizing the [[elementary embedding]] characterization of measurable cardinal, a cardinal $\kappa$ is ''$\theta$-supercompact'' if there is an elementary embedding $j:V\to M$ with $M$ a transitive class, such that $j$ has critical point $\kappa$ and $M^\theta\subset M$, i.e. $M$ is closed under […]Julian Barathieu
- Strongly compact← Older revision Revision as of 12:59, 19 November 2017 Line 60: Line 60: If there is a strongly compact cardinal $\kappa$ then for all $\lambda\geq\kappa$ and $A\subseteq\lambda$, $\lambda^+$ is [[ineffable]] in $L[A]$. If there is a strongly compact cardinal $\kappa$ then for all $\lambda\geq\kappa$ and $A\subseteq\lambda$, $\lambda^+$ is [[ineffable]] in $L[A]$. −It is not […]Julian Barathieu
- Ultrapower axiomRedirected page to Ultrapower#Ultrapower axiom New page#REDIRECT [[Ultrapower#Ultrapower axiom]]Julian Barathieu

- Ultrapower

# Monthly Archives: July 2009

## Ramsey-like Cardinals II

V. Gitman and P. D. Welch, “Ramsey-like cardinals II,” The journal of symbolic logic, vol. 76, iss. 2, pp. 541-560, 2011. PDF Journal MR Citation arχiv @ARTICLE{gitman:welch, AUTHOR= "Victoria Gitman and Philip D. Welch", TITLE= "Ramsey-like cardinals {II}", JOURNAL … Continue reading