# Tag Info

### On the intersection of finitely many ultrafilters

There is a category theoretic characterization of the filters that can be written as intersections of finitely many ultrafilters. I claim that a filter $Y$ on $G$ is the intersection of finitely many ...

### On the intersection of finitely many ultrafilters

Let me try to provide a helpful elementary answer. Suppose that $F$ is a filter on a set $X$ arising as the intersection of finitely many ultrafilters $$F=\mu_1\cap\cdots\cap\mu_n.$$ We may assume ...

### Is every sigma-algebra the Borel algebra of a topology?

If $\Sigma$ is countably generated -- and any sigma-algebra of practical interest will be [Edit: or will be the completion of such an algebra] -- then I believe the answer is yes. Here is the argument....
Accepted

### Strength of Borel determinacy

I don't know why you would want to work with $\mathrm{ZC}^{-}$, this is not a theory I would recommend to do math in. But as long as you only care about second order number theory, there is really no ...

### Can set theory be interpreted in infinite arithmetic?

Without considering your system of arithmetic too closely, let me mention that ZFC is interpretable in Peano arithmetic, if one augments PA with the assertion that ZFC is consistent. That is, ZFC is ...

Accepted

### (Very) Large numbers, Chaitin's incompletness theorem and a specific upper bound

One way to provide an explict bound on $L$ is as follows, using the idea of the universal algorithm. Namely, for any computably axiomatizable theory $T$ in question, consider the algorithm $p$ that ...

Accepted

### Is the set of permissible numbers of models of various cardinalities computable?

Let $T$ be a complete countable first-order theory. I will write $I(T,\kappa)$ for the number of models of $T$ of cardinality $\kappa$ up to isomorphism. The function $I(T,-)$ is called the spectrum ...

### Set theories without "junk" theorems?

Junk theorems like this are avoided in Type Theory (not just HoTT). This is because I cannot talk about the representation of objects like the natural numbers. This is exploited in Homotopy Type ...
In Chapter 3 of his PhD thesis, Harvey Friedman showed that there is a recursive linear ordering $\prec$ which has no hyperarithmetic infinite descending sequence and which does not support a jump ...
The Parity Principle follows from the axiom $\mathbf C_2$ (defined below) which is weaker than the Axiom of Choice. I don't know whether the Parity Principle implies $\mathbf C_2$, but that's another ...