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I am quite new at nonstandard analysis, and recently I became aware of its use in probability theory mainly through the following two books:
Nelson (1987). Radically Elementary Probability Theory
Geyer (2007). Radically Elementary Probability and Statistics...

The 4$^{th}$ of https://en.wikipedia.org/wiki/Landau%27s_problems is on the infinity of primes that are one more than a square.
The answer depends on certain assumptions about allowable statements and how size is measured.Here, I restrict statements to be constructed from Peano arithmetic (0, s, +, $\times$) using = and $\neq$and quantifiers but without logical operators (and...

This question is reposted from SE, where I have not received an answer. I am happy to delete this if I get an answer there.
This question comes from Kollar-Mori's book Birational geometry of algebraic varieties Example 2.7 pp 39-41.
Let $Y = \mathrm{Spec}(\mathbb{C}[x,y,u,v]/xy=uv)$ and let $X$ be the blowup of $Y$ along the ideal $(x,v)$. We can represent a point of $X$ as a tuple $((x,y,u,v),[s:t])$ satisfying $xt=vs$ (among others). Consider the action of $\mu_n$ on $X$, where...

This is a follow-up to the last part of an old MSE answer of mine. Briefly, an analogue at $\omega_1$ of Steel's equivalence between clopen and open determinacy can be proved assuming $\mathsf{CH}$, and I'm curious whether that's necessary.
Let $C_{\omega_1}$ be the set of subtrees of ${\omega_1}^{<{\omega_1}}$ thought of as open games on ${\omega_1}$ of length ${\omega_1}$: there are two players $1$ and $2$ who alternately play elements of $\omega_1$ for $\omega_1$-many rounds with...