A clonoid based approach to some finiteness results in universal algebraic geometry
Erhard Aichinger, Bernardo Rossi · Algebra Universalis · 2020
Abstract We prove that for a finite first order structure $${\mathbf {A}}$$ A and a set of first order formulas $$\Phi $$ Φ in its language with certain closure properties, the finitary relations on A that are definable via formulas in $$\Phi $$ Φ are uniquely determined by those of arity $$|A|^{2}$$ |A|2 . This yields new proofs for some finiteness results from universal algebraic geometry.