### 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

- IndescribableAdded consistency strength notes ← Older revision Revision as of 23:08, 19 October 2017 Line 7: Line 7: In other words, if a cardinal is $\Pi_{m}^n$-indescribable, then every $n+1$-th order logic statement that is $\Pi_m$ expresses the reflection of $V_{\kappa}$ onto $V_{\alpha}$. This exercises the fact that these cardinals are so large they almost […]Zetapology
- Axiom of determinacy← Older revision Revision as of 18:26, 19 October 2017 (14 intermediate revisions by the same user not shown)Line 41: Line 41: * The reals cannot be well-ordered. Thus the full [[axiom of choice]] fails. * The reals cannot be well-ordered. Thus the full [[axiom of choice]] fails. * Every set of real is [[:wikipedia:Lebesgue measurable|Lebesgue […]Wabb2t
- ReflectingAdded small remark of $\aleph$-fixed point-ness ← Older revision Revision as of 03:56, 13 October 2017 Line 13: Line 13: * A simple Löwenheim-Skolem argument shows that every infinite cardinal $\kappa$ is $\Sigma_1$-correct. * A simple Löwenheim-Skolem argument shows that every infinite cardinal $\kappa$ is $\Sigma_1$-correct. * For each natural number $n$, the $\Sigma_n$-correct cardinals form […]Zetapology

- Indescribable

# Monthly Archives: April 2015

## An introduction to nonstandard models of arithmetic

This is a talk at the Virginia Commonwealth University Analysis, Logic and Physics Seminar, April 24, 2015.

Posted in talks
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