7 problems

Ordered-group projective-plane conjecture. An ordered abelian group cannot locally trace define an infinite projective plane.

Invariant-subsemigroup separation conjecture. For every $P\subseteq C^+$ such that $P$ and $C^+\setminus P$ are closed under concatenations and cyclic shifts, there exists an invar…

ETOG representation conjecture. Every bi-positional prefix-independent winning condition coincides on periodic sequences with some energy condition over a totally ordered group.

Positive-relator quotient conjecture.

Ordered-abelian-group conjecture. An ordered abelian group cannot trace define an infinite field.

Let $X$ be a totally ordered Abelian group with respect to addition, and let $F:X^n\to X$ be an associative, idempotent, monotone function. The function $F$ is reducible if there e…

Let $\nu:F^*\rightarrow\mathbb{Z}^n$ be a maximal valuation, and let $\mathcal{O}=\{f\in\mathscr{F}:\nu(f)\geq 0\}$ with maximal ideal $\mathcal{m}=\{f\in\mathscr{F}:\nu(f)>0\}$ in…