There are a number of postulates that have been studied in constructive math that are anti-classical in the sense that they are demonstrably false in classical logic: for example, the postulate that “

In the category of assemblies over Kleene's first algebra $\mathcal{K}_1$ (or in the corresponding realizability topos, namely the effective topos), the natural numbers object $ℕ$ is carried by $ℕ$

This PR fixes a soundness issue. TL;DR. The kernel's is_prop decided whether a term is a proposition by taking the weak head normal form of its inferred type and checking that the result is syn...

Let me first clarify that I am not expecting the titular question to have a single well-defined answer (or it would probably have to be a useless one like “the topos freely generated by the followi...

Given polynomials $f_{1},\cdots,f_{n}\in \mathbb{C}[x_{1},\cdots,x_{m}]$, do we have an algorithm to determine whether the ideal $I=(f_{1},\cdots,f_{n})$ is prime ideal or not? Of course, we assume...

Recall that a morphism $f\colon X\to Y$ of locales is said to be open when its inverse image part $f^*\colon \mathcal{O}(Y) \to \mathcal{O}(X)$ (where $\mathcal{O}(X)$ denotes the frame of opens wh...

Most of us know the Jacobian conjecture. Here's a version below for fixed positive integers $d$ and $n$: $J(d,n)$: If $f: C^n \rightarrow C^n$ is a polynomial map of degree $d$, and if the Jacob...