Recent Writing- Mathoverflow Activity
- 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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Monthly Archives: January 2013
Models of Peano Arithmetic
…it’s turtles all the way down. In 1889, more than two millennia after ancient Greeks initiated a rigorous study of number theory, Guiseppe Peano introduced the first axiomatization for the theory of the natural numbers. Incidentally, Peano is also famous … Continue reading
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The Completeness Theorem
The Completeness Theorem was proved by Kurt Gödel in 1929. To state the theorem we must formally define the notion of proof. This is not because it is good to give formal proofs, but rather so that we can prove … Continue reading
Posted in logic.2013
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