（念のため英文） https://en.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem Lowenheim-Skolem theorem Consequences The statement given in the introduction follows immediately by taking M to be an infinite model of the theory. The proof of the upward part of the theorem also shows that a theory with arbitrarily large finite models must have an infinite model; sometimes this is considered to be part of the theorem.
