We consider a φ-logic L(ω) of a frame of order type ω endowed with an irreflexive operator. The irreflexive modality in LC was treated by the author in [Sib. Math. J., 55, No. 1, 185-190 (2014)] where it was shown that this modality on the class of finite chains, on the one hand, and on a single chain of order type ω, on the other hand, generates inconsistent φ-logics over LC. There, also, it was stated that L(ω) defines a new nonconstant connective in LC. Here we establish that the φ-logic L(ω) is Novikov complete over LC.

中文翻译：

---

ω型和PS Novikov完整性链上的不自反模态

我们考虑赋予非自反算子的阶数类型为ω的帧的逻辑L（ω）。在[Sib。数学。J.，55，No. 1，185-190（2014）]，其中证明了这种形式一方面是在有限链类上，另一方面是在阶数为ω的单链上，在LC上产生不一致的φ逻辑。在那里，据称L（ω）在LC中定义了一个新的非恒定连接词。在这里，我们确定φ-逻辑L（ω）在LC上是Novikov完备的。