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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: talks

## Virtual large cardinal principles at KGRC

This is a talk at the Kurt Gödel Research Center Research Seminar in Vienna, Austria, April 14, 2018.

Posted in talks
Tagged forcing, Generic Vopěnka’s Principle, virtual large cardinals
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## The emerging zoo of second-order set theories

This is a talk at the Young Researchers’ Workshop: Forcing and Philosophy, University of Konstanz, January 18, 2018.

## Virtual large cardinal principles

This is a talk at the Harvard Logic Colloquium, Cambridge, November 8, 2017.

Posted in talks
Tagged forcing, Generic Vopěnka’s Principle, large cardinals, virtual large cardinals
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## Filter games and Ramsey-like cardinals

This is a talk at the CUNY Set Theory Seminar, October 20, 2017.

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## A model of second-order arithmetic with the choice scheme in which $\Pi^1_2$-dependent choice fails

This is a talk at the Kurt Gödel Research Center Research Seminar in Vienna, Austria, May 18, 2017.

## Computable processes which produce any desired output in the right nonstandard model

This is a talk at the special session “Computability Theory: Pushing the Boundaries” of 2017 AMS Eastern Sectional Meeting in New York, May 6-7.

## Virtual Set Theory and Generic Vopěnka’s Principle

This is a talk at the VCU MAMLS Conference in Richmond, Virginia, April 1, 2017.

## A countable ordinal definable set of reals without ordinal definable elements

This is a talk at the CUNY Set Theory Seminar, February 10, 2017.

## A set-theoretic approach to Scott’s Problem

This is a talk at the National University of Singapore Logic Seminar, October 19, 2016.

Posted in talks
Tagged Ehrenfeucht's lemma, PFA, proper families of reals, scott sets
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## Generic Vopěnka’s Principle at YST2016

This is a talk at the Young Set Theory 2016 Conference in Copenhagen, Denmark, June 13-17, 2016.