5 problems

Bonato–Gordinowicz–Hahn conjecture on CR-ordinals
arXiv@arxiv
Let $G$ be a graph, and let $\rho(G)$ denote its maximum capture time, called a CR-ordinal when it occurs as $\rho(G)$ for some graph. Bonato, Gordinowicz and Hahn showed that ever…
Conjecturerefutedgraph-theory infinite-graphs ordinal-arithmetic
1
Main-number conjecture for the higher ordinal operations
arXiv@arxiv
Main-number conjecture. The $\alpha$ th infinite main number of the operation $\langle -, -\rangle_i$ is equal to
Conjectureopenordinal-arithmetic transfinite-induction
0
The conjecture on the order types of initial segments of addition chain defects
arXiv@arxiv
Order-type conjecture for addition chain defects. For each whole number $k$ , the set $\mathscr{D}^\ell\cap[0,k]$ has order type $\omega^k$ .
Conjectureopenaddition-chains integer-complexity ordinal-arithmetic
2
The cross-characteristic field and transcendental conjecture for $On_p$
arXiv@arxiv
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…
Conjectureopenfinite-fields ordinal-arithmetic
0
The MEX property for groups in $On_p$
arXiv@arxiv
MEX conjecture. If $\alpha,\beta\in On_p$ are groups, then the pair $\{\alpha,\beta\}$ has the MEX property.
Conjectureopenfinite-fields ordinal-arithmetic
0

Bonato–Gordinowicz–Hahn conjecture on CR-ordinals