14 problems

Let $X$ be a finite CKL-algebra, meaning an L-algebra satisfying the CKL axioms. Call $X$ simple if it has no nontrivial ideals, and call it linear if its underlying order is linea…

A CKL-algebra is an algebra in the class of L-algebras satisfying the CKL axioms; an L-algebra is simple when it has no nontrivial ideals, and it is linear when its underlying orde…

Let \text{{mathcal Fm}}^+\!\slash\!\!\equiv be the formula-algebra expanded by transposition operations and quotiented by semantic equivalence, and let \text{{mathcal Fm}…

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…

Let $A$ be the algebra constructed in Section 4, and let $G$ be the Galois algebra constructed by Galatos and Jipsen. Isomorphism conjecture. The algebra $A$ is isomorphic to $G$.…

Non-surjectivity conjecture. Not all $\mathcal{L}_\bullet$-sequents have their algebraic correspondents in $\mathcal{L}_\mathrm{SI}$.

Non-correspondence conjecture. The sequents (Sym), (Euc) and (D) never correspond to any $\mathcal{L}_\bullet$-sequents.

Fixed-variable tractability conjecture. For each fixed number of variables, the decision problem admits a more tractable decision procedure.

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…

Rainbow indistinguishability conjecture. The two algebras cannot be distinguished by any $n$-variable diagonal-free equation.

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…

Let a monadic De Morgan reduct be the reduct of a suited IFG$_1$-algebra to the signature … Let $\mathcal K^{\nabla_1}$ be the variety defined in the surrounding algebraic framewor…