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- Comment by Victoria Gitman on Consistency strength of the existence of a transitive model of $\mathsf{ZFC}^-$ with a $\kappa$-complete ultrafilterThis is really very nice!Victoria Gitman
- Comment by Victoria Gitman on Consistency strength of the existence of a transitive model of $\mathsf{ZFC}^-$ with a $\kappa$-complete ultrafilterAli, I am just seeing the comment because I have been away from MO for a while. So you are saying that even an ill-founded ultrapower by a non-normal filter as long as it is weakly amenable can be used to show that kappa is weakly compact in M?Victoria Gitman
- Answer by Victoria Gitman for Consistency strength of the existence of a transitive model of $\mathsf{ZFC}^-$ with a $\kappa$-complete ultrafilterLet's make some additional assumptions on the ultrafilter $U$. Suppose $M\models{\rm ZFC}^-$ and $\kappa$ is a cardinal in $M$. We say that $U$ is an $M$-ultrafilter if $\langle M,\in,U\rangle$ satisfies that $U$ is a $\kappa$-complete normal ultrafilter on $\kappa$. Because $U$ is only $\kappa$-complete for sequences in $M$ and $M$ might be missing even countable […]Victoria Gitman

- Comment by Victoria Gitman on Consistency strength of the existence of a transitive model of $\mathsf{ZFC}^-$ with a $\kappa$-complete ultrafilter
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# Category Archives: personal

## Co-organizing the CUNY Set Theory Seminar

I was lucky enough to start graduate school and end up choosing the same adviser with two people who still remain my favorite colleagues and dearest friends. Coincidentally, the adviser also turned out to be quite good. The students were … Continue reading

Posted in personal, research
Tagged CUNY Set Theory Seminar, J. D. Hamkins, J. Reitz, T. Johnstone
4 Comments

## A Gilmore girl moment

I just got back from giving a talk at UConn on incomparable $\omega_1$-like models of set theory. (Please note that there will be no mathematical content beyond this point. I allow myself a personal post once every few years, whenever … Continue reading

Posted in personal
6 Comments

## On ground model definability: completed!

The final version of the “On ground model definability” paper is here! If interested, please check the updated version of the related post or the PDF of the paper.

Posted in personal
4 Comments

## Who let the zombies out?

Academic writing, whether it be a math article or a philosophy textbook, most often fails to capture our imagination or even keep us awake long enough to trudge through its convoluted contents. In unlocking the universe’s greatest mysteries, these treatises … Continue reading

Posted in personal
5 Comments

## Two perspectives on Halloween

I went trick-or-treating for the first time this Halloween, twenty years since coming to the United States. Incidentally, according to Wikipedia, Halloween has its origins in the celtic festival Samhain, a harvest celebration and a time to honor the dead.

Posted in personal
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