MathOverflow

The (second-order) Baire category theorem for open sets given by codes is provable in the base theory RCA$_0$ of reverse mathematics (see Simpson's SOSOA).
Is the following version of the Baire category theorem provable in ACA$_0$?
Let $\varphi$ be an arithmetical formula satisfying...

Sorry if this is easy for MathOverflow, the problem I have is inverting the following sum
\begin{align*}S &= \sum_{i_1=0}^{r_1} \sum_{i_2=0}^{r_1+r_2-i_1} \cdots \sum_{i_{n-1}=0}^{r_1+\cdots+r_{n-1}-i_{n-2}} \\&\quad (-1)^{i_1+\cdots+i_{n-1}} \quad (r_1)_{i_1} (r_1+r_2-i_1)_{i_2} \cdots (r_1+\cdots+r_{n-1}-i_{n-2})_{i_{n-1}} \\&#...

I have recently been trying to compute an explicit bound on the number of blow ups required to resolve a singular variety $X$ of degree $d$ in $\mathbb{P}^n$, depending only on $d$ and $n$. I am trying to use the techniques of the recent paper on Effective...

Given a complex surface germ $(X,0)$ which is seminormal, consider its normalization$$n : (\overline{X},0) \longrightarrow (X,0).$$Is the normalization map $n : \overline{X} \to X$ an immersion, that is, does its differential have trivial kernel at every...