MathOverflow

In the study of integer dynamical systems related to the Collatz map, consider the operator
$$E(n) = \frac{3n+1}{2^{v_2(3n+1)}}$$
and its iterates

Let $\mathsf{Groups}(X)$ denote the set of groups with underlying set $X$. Cayley's theorem does not use choice: it is a theorem of $\mathsf{ZF}$ that, for every set $X$, there is a function $i:\mathsf{Groups}(X)\rightarrow (S_X)^X$ such that, whenever...

Given a finite set of $n \times n$ integer matrices it's known (the "Mortality Problem") that for $n > 2$ the problem of determining whether a finite product of them is the 0 matrix is undecidable. I'm interested in an analogous problem: determine...

While trying to gain some understanding on how extensional realizability relates to the reg/lex and ex/lex completions of assemblies, I came to believe the following mutually contradictory statements (definitions to be provided below):
The reg/lex construction $(\mathbf{Ass})_{\mathrm{reg/lex}}$ on the category $\mathbf{Ass}$ of assemblies gives (a category equivalent to) the category $\mathbf{ExtAss}$ of extensional assemblies....