Categoricity and quantifier elimination for intuitionistic theories

Some preservation theorems in an intermediate logic

“…Such a sequence is called an elementary chain if A i ≤ A j whenever i ≤ j. The following result is proved in [1]. …”

“…To start with, we review some notions from intuitionistic logic (we do not consider the general case) and also some results from [1]. As usual, ∧, ∨, ⇒, ≡, ∃ and ∀ are used as primitive logical symbols for intuitionistic logic (we keep → for another usage).…”

“…Then ϕ ⇒ ∃x ψ is logically equivalent to an existential formula and ϕ ⇒ ∀x ψ is logically equivalent to a universal formula. [1]). Take a model A = (A α ) α∈k of T and for each α ∈ k set A α = (A β ) β α .…”

“…In this paper we consider the class of semi-classical models introduced in [1]. A semi-classical model is a Kripke model whose frame is a linear order, has a constant domain and whose nodes have presentation by atomic formulas.…”

“…In the next section we shortly review some results from [1]. In the third section we study preservation theorems with emphasis on the notions of model-completeness and inductiveness.…”