Satisfiable first-order theory
= Satisfiable first-order theory
= Satisfiable
{synonym}
A set of first-order sentences is satisfiable when it has a nonempty structure in which all its sentences are true. Truth of a sentence is independent of <assignment in a first-order structure>. The <soundness theorem for first-order logic> gives consistency from satisfiability, and <Gödel's completeness theorem> gives the converse for the standard classical deductive system.