We extend the notion of Heyting algebra to a notion of truth values algebra and prove that a theory is consistent if and only if it has a B-valued model for some non trivial truth values algebra B. A theory that has a B-valued model for all truth values algebras B is said to be super-consistent. We prove that super-consistency is a model-theoretic sufficient condition for strong normalization.

翻译：我们将海廷代数的概念推广至真值代数的概念，并证明一个理论是一致的当且仅当它对某个非平凡真值代数B具有B-值模型。一个理论若对所有真值代数B均具有B-值模型，则称其为超一致的。我们证明超一致性是强规范化的一个模型论充分条件。