Diagram Construction in Intuitionistic Logic

Omitting Types in an Intermediate Logic

“…Using normal forms one sees that if f preserves basic semi-atomic formulas it is an embedding. In fact one may freely use classical properties of diagrams in a modified form (see [3,4]). Here, our aim is to prove an omitting types theorem for semi-classical theories.…”

“…∈ k) is a semi-classical model (see [4] for further details). We prove by induction on the complexity of φ that for each atomic θ:…”

“…However, not all these generalizations behave well. In [2], [3] and [4] we studied a particular intermediate logic very close the classical one in which the notion of embedding behaves well. In this logic, categoricity does make sense and interesting preservation theorems hold.…”