# Definition A [[forcing#^e01f21|forcing notion]] $\mathbb{P}$ with top element $\mathbb{1}$ satisfies the *zero-one law* if for every sentence $\varphi$, $\mathbb{1}\Vdash \varphi$ or $\mathbb{1}\Vdash \neg \varphi$. # Properties # Relations ## Implied by - [[Homogeneity|Weakly homogeneous]] ## Implies - [[]] # Preservation