Recent Writing- 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
- Computable processes which produce any desired output in the right nonstandard model
- Virtual large cardinals
- 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
- JonssonRelations to other large cardinal notions ← Older revision Revision as of 12:04, 22 July 2017 Line 30: Line 30: Jónsson cardinals have a lot of consistency strength: Jónsson cardinals have a lot of consistency strength: * Jónsson cardinals are equiconsistent with Ramsey cardinals (Mitchell, 1999). * Jónsson cardinals are equiconsistent with Ramsey cardinals (Mitchell, 1999). −* […]Dan Saattrup Nielsen
- Jonsson
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
Posted in logic.2013
Leave a comment
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
Leave a comment