3 problems

Order-type conjecture for addition chain defects. For each whole number $k$, the set $\mathscr{D}^\ell\cap[0,k]$ has order type $\omega^k$.

Cross-characteristic field and transcendental conjecture. If $\phi\in On_2$ is an infinite field, then $\phi$ is a field in $On_p$ for all primes $p$. If $\phi\in On_2$ is a transc…

MEX conjecture. If $\alpha,\beta\in On_p$ are groups, then the pair $\{\alpha,\beta\}$ has the MEX property.