5 problems

Let $S_n$ be a syntactic fractal space with a family of definable sets $cF_n$, and let $\nu_n$ and $\mu_n$ be $S_n$-measures. Write $\nu_n \ll \mu_n$ when $\mu_n(A)=0$ implies…

Cauchy-completeness separation conjecture. 1. There exists an elementary topos in which $\mathbb{R}_C\neq\mathbb{R}_E$; equivalently, there exists an elementary topos in which…

Propositional-canonicity conjecture. The context $(x:\mathbf{LLPO}_\vee)$ has propositional canonicity for $\mathbb{N}$ over type theory with bracket types, as studied by Awodey an…

Let a topos with natural number object be a topos equipped with a natural number object, and let a monic polynomial with reductions be as considered in the paper. Initial-algebra f…

A W-pretopos is a category with the structural properties implicit in the paper, and WISC denotes the weak internal axiom of choice used there. Free algebra existence conjecture. F…