11 problems

Isomorphism conjecture. There is an isomorphism

Let $\gamma$ be an ordinal with Cantor normal form, and write $\alpha_1$ for its leading exponent. Let $\beta(\gamma)$ be the corresponding beta space, $sf L(\beta(\gamma))$ its logic, a…

Let $(a_\alpha)_{\alpha<\xi}$, $(b_\alpha)_{\alpha<\xi}$, and $(c_\alpha)_{\alpha<\xi}$ be the transfinite sequences associated with the three complexity classes modulo $3$. Block-…

Let $\|n\|$ denote the complexity of a natural number, and let $\xi$ be an ordinal. Consider three transfinite sequences $(a_\alpha)_{\alpha<\xi}$, $(b_\alpha)_{\alpha<\xi}$, and…

Arias's conjecture. The set $A$ has finite symmetric difference with $E$, and the one-sided difference $A\setminus E$ is a finite subset of

Let $T$ be a strong system with an ordinal analysis based on ordinal representation systems $\mathsf{OT}$. These systems give rise to functors … that send dilators to ordinal repre…

Interval representation conjecture. Every fusible number in $I_{x,n}$, for $n\geq 1$, can be written as

Let $\uppsi_0$ be the ordinal collapsing function and let $\cond_{\top}$ denote the corresponding worm/spider collapsing operation. The first collapsing-function identity. One has…

For infinite chess, let $\omega_1^{\mathfrak{Ch}}$ be the supremum of game values for positions with at most finitely many pieces, let $\omega_1^{{\mathfrak{Ch}},c}$ and…

Let ${\mathcal{F}}$ be the set of fusible numbers. For $a\in{\mathcal{F}}$, let $s(a)$ be its successor, let $m(a)$ denote the relevant minimum gap, and write … as before. Main con…

A well-founded tree is a prefix-closed set of finite sequences, and its order type is the ordinal order type used in the paper. A coloring of such a tree assigns each node one of t…