MathOverflow

Previously asked at MSE without success:
Consider the following statement:
$(*)\quad$ There are $\omega$-models of ZFC of arbitrarily large cardinality.

Consider $n$ switches arranged in a circle, each initially either ON (1) or OFF (0), with all $2^n$ configurations equally likely.
At each step, all switches are updated simultaneously according to the following rule:a switch is set to ON if its two neighbors were in the same state at the beginning of the step; otherwise, it remains in its current state.This operation is then iterated...

Let $ \sigma \geq \frac{n}{2} $. And consider the inhomogeneous Besov space $B^{\sigma}_{2,1}$ with the norm$$ \Vert f \Vert_{B^{\sigma}_{2,1}}= \sum_{k=0}^{\infty} 2^{\sigma k} \Vert \Delta_{k} f \Vert_{L^{2}} $$ with the understanding that $ \Delta...

Let $X$ be a finite set. Recall that a binary operation $\ast$ on $X$ is said to be a quasigroup operation if there are binary operations $/,\backslash$ where $(x/y)\ast y=(x\ast y)/y=x$ and $x\ast(x\backslash y)=x\backslash(x\ast y)=y$.
Let $T:X^2\rightarrow X^2$ be a bijection. Let $\ast_{l,+},\ast_{l,-},\ast_{r,+},\ast_{r,-}$ be the binary operations where $T(x,y)=(x\ast_{l,+}y,x\ast_{r,+}y),T^{-1}(x,y)=(x\ast_{l,-}y,x\ast_{r,-}y)$ whenever $x,y\in X$. Then we say that $T$ is a well...