13 problems

Flexible Atom Conjecture. Every finite integral relation algebra with a flexible atom is representable over a finite set.

NP-membership conjecture. The network satisfaction problem of $\mathbf{56}_{65}$ is in $\operatorname{\mathbf{NP}}$.

Tractability conjecture. If $\mathfrak{B}$ does not pp-construct $(\{0,1\};\operatorname{NAE})$, then

A finite relation algebra is a finite algebra equipped with the Boolean operations, relational composition, converse, and identity element satisfying the relation-algebra axioms; i…

Let $\mathcal{L}$ be any conception of a set algebra corresponding to the notion of satisfaction, and let $\mathcal{L}'$ be the corresponding class for any choice of basic operatio…

A relation algebra is an algebraic structure with the operations used to express the equational form of first-order logic; a class is finitely axiomatizable if it can be defined by…

Siggers-behavior conjecture. Dropping the requirement that ${\bf A}$ has all $1$-cycles should yield a necessary and sufficient condition for solvability of…

Finite representation property conjecture. The signature $\tau$ has the finite representation property if and only if

Flexible atom conjecture. Every finite integral relation algebra with a flexible atom is representable over a finite set.

Non-derivability conjecture. This equation does not follow from the axioms presented in the cited theorem.

Let $k$ denote the parameter used for the witness in the surrounding construction, and let Jonsson's $Q$'s denote the corresponding family of candidate structures. Jonsson-$Q$ witn…

The discussion concerns relation algebras and the construction of concrete witnesses with finite atom structures. Relation-algebra witness conjecture. The authors conjecture that t…

Strong representability conjecture for $\alpha({\bf G})$. The relation-algebra atom structure $\alpha({\bf G})$ is strongly representable if and only if ${\mathfrak{M}}({\bf G})$ i…