5 problems

Let $\mathbf{A}$ be the core of a reduct of a finitely bounded homogeneous structure. A pseudo-Siggers identity is an identity of the form … where $s$ is a 6-ary polymorphism and…

Let $n\geq 4$, let $\mathbb{G}$ be an $n$-cycle, and let $f$ be a surjective homomorphism from a product of subpaths of $\mathbb{G}$ of length $n-2$ to $\mathbb{G}$. An edge $e$ of…

Let ${\mathfrak B}$ be a countable $\omega$-categorical model-complete core. A polymorphism is an operation preserving all relations of ${\mathfrak B}$, and an endomorphism is a un…

Let ${\mathfrak B}$ be a countable $\omega$-categorical model-complete core, and let $f$ be an $n$-ary polymorphism of ${\mathfrak B}$. Cyclic polymorphism conjecture. If, for ever…

Let $\Gamma$ be an $\omega$-categorical structure with finite relational signature. A family of totally symmetric polymorphisms consists of polymorphisms of every arity whose value i…