### Recent Writing

- 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
- Computable processes which produce any desired output in the right nonstandard model
- Virtual large cardinals
- Virtual Set Theory and Generic Vopěnka’s Principle

### 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

- BerkeleyAdded that the critical point of j can be arbitrary large above kappa. Removing this notion results in a "Proto-Berkeley" cardinal. Source: http://logic.harvard.edu/blog/wp-content/uploads/2014/11/Deep_Inconsistency.pdf ← Older revision Revision as of 14:40, 23 June 2017 Line 1: Line 1: −A cardinal $\kappa$ is a ''Berkeley'' cardinal, if for any transitive set $M$ with $\kappa\in M$, there is […]Dan Saattrup Nielsen

- Berkeley

# Monthly Archives: March 2013

## Tennenbaum’s Theorem

Gödel’s Incompleteness Theorems established two fundamental types of incompleteness phenomena in first-order arithmetic (and stronger theories). The First Incompleteness Theorem showed that no recursive axiomatization extending ${\rm PA}$ can decide all properties of natural numbers and the Second Incompleteness Theorem … Continue reading

Posted in logic.2013
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## Order amidst the chaos: exploring Julia sets and the Mandelbrot set

This is a project with Mariama Wilson.

Posted in student projects
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## The Second Incompleteness Theorem

There is a theory which states that if ever anyone discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory … Continue reading

Posted in logic.2013
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## The First Incompleteness Theorem

Some people are always critical of vague statements. I tend rather to be critical of precise statements; they are the only ones which can correctly be labeled ‘wrong’. –Raymond Smullyan At the dawn of the $20^{\text{th}}$-century formal mathematics flourished. In … Continue reading

Posted in logic.2013
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