Omitting types of prenex formulas
Chen Chung Chang · Journal of Symbolic Logic · 1967
In the literature, a type Γ is a set of formulas ϕ(ν0) in the one free variable ν0. A model M realizes Γ if there is an element a of M such that M ╞ ϕ [a] for all ϕ ∈ Γ. A model M omits Γ if no element of M realizes Γ. Evidently, the two statements: (*) M realizes Γ and (**) M omits Γ