4 problems

Let $M$ be a countable recursively saturated model of $\mathrm{PA}$, and let $\operatorname{SSy}(M)$ denote its standard system. Transcendence characterization conjecture. There is…

The thesis studies recursive saturation, arithmetic saturation, and stronger expandability properties for models of arithmetic, where an expansion is required not only to satisfy a…

Let $\mathcal{M}$ be a countable recursively saturated model of $\mathrm{PA}$, let $\mathrm{G}:=\operatorname{Aut}(\mathcal{M})$, and let $I$ be a cut of $\mathcal{M}$. Define … Th…

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