3 problems

Khoussainov's conjectures. (1) No nonstandard model of arithmetic admits a computable quotient presentation by a computably enumerable equivalence relation on the natural numbers.…

Let a finitely generated group have a $\Pi^0_1$ word problem, meaning that its word problem is a co-c.e. equivalence relation on words, but suppose it is not isomorphic to a finite…

Let $M$ and $N$ be finite-dimensional $\mathbb{R}$-computable $\mathbb{R}$-vector spaces with the same dimension. Computable categoricity conjecture. There should be a $\mathbb{R}$…