4 problems

Let $m\geq 1$. Write $\mathcal{A}_{m+1}$ for the canonical tree of rank $m+1$, and let $B^{(m)}_j:=[m+1:j]$ be the tree obtained by deleting all but $j$ of the level-one subtrees o…

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 $G$ be a finitely presented computable group. A computable $d$-$\Sigma_2$ Scott sentence is a Scott sentence for $G$ that is the conjunction of a computable $\Sigma_2$ sentence…

Let $G$ be a computable connected graph whose distance function is intrinsically $n$-approximable from above, where $n>0$. A function is $n$-approximable from above if it has an ap…