4 problems

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Finite axiomatizability of transposition operations over the semantic formula-algebra
Let $\text{$ {mathcal Fm} $}^+\!\slash\!\!\equiv$ be the formula-algebra expanded by transposition operations and quotiented by semantic equivalence, and let $\text{$ {mathcal Fm}…
Conjectureopenalgebraic-logic finite-axiomatizabilityarXiv posted 2 days ago
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Monk's conjecture on the non-finite axiomatizability of equational first-order logic
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…
Conjecturesolvedalgebraic-logic finite-axiomatizability relation-algebrasarXiv posted 2 days ago
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Monk's conjecture on the non-finite axiomatizability of representable relation algebras
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…
Conjecturesolvedalgebraic-logic finite-axiomatizability relation-algebrasarXiv posted 2 days ago
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The BSS conjecture on finite axiomatisability and elementarity
A class of modal logics is considered in which the relevant logics are defined by first-order conditions of the form $\forall x\exists y\,(xR_\lambda y\land\phi(y))$ , where…
Conjectureopenelementarity finite-axiomatizability modal-logicarXiv posted 2 days ago

Finite axiomatizability of transposition operations over the semantic formula-algebra