Łoś–Vaught test
In model theory, a branch of mathematical logic, the Łoś–Vaught test is a criterion for a theory to be complete, unable to be augmented without becoming inconsistent. For theories in classical logic, this means that for every sentence, the theory contains either the sentence or its negation but not both.
Statement
A theory with signature σ is -categorical for an infinite cardinal if has exactly one model of cardinalityThe Łoś–Vaught test states that if a first-order satisfiable theory is -categorical for some and has no finite model, then it is complete.
This theorem was proved independently by and, after whom it is named.