Interpolation property and homogeneous structures
Zalán Gyenis · Logic Journal of IGPL · 2014
This article introduces a local variant of Craig's interpolation: a model M is said to have the interpolation property if for certain formulae M⊧ϕ → ψ implies the existence of an interpolant formula ϑ in the intersection of the languages of ϕ and ψ such that M⊧ϕ → ϑ and M⊧ϑ → ψ. A new amalgamation property is also introduced and it is shown that in the context of certain universal homogeneous structures, this special amalgamation property is equivalent to interpolation property.