A clonoid based approach to some finiteness results in universal algebraic geometry

Abstract

We prove that for a finite first order structure $\mathbf{A}$ and a set of first order formulas $\Phi$ in its language with certain closure properties, the finitary relations on $A$ that are definable via formulas in $\Phi$ are uniquely determined by those of arity $|A{|}^2$. This yields new proofs for some finiteness results from universal algebraic geometry.

Cited by in corpus (1)

• On when the union of two algebraic sets is algebraic