Model Theory for Modal Logic pp 63-67 | Cite as

# Model Extensions

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## Abstract

Let 𝕬 and 𝔅 be modal structures for ML and let *m*: 𝕬 → 𝔅. If *m* is a *Γ*-morphism we say that 𝔅 is a *Γ*-*extension of* 𝕬 *via m*. A set *Γ* of formulas of ML is said to be *regular* if it includes all formulas of the forms x = y and A_{x1}…_{xn}[y_{1}…y_{n}] whenever it comtains A. A formula A of ML is said to be a * *-*formula* if it is obtained from a formula of the form θ _{h} ^{*} (cf. Definition 6.8), where *h* was a basic formula bundle over *𝕬*, by replacing all names of elements of |*𝒜* _{0}| by free variables (so that ∧*h* _{2}(O) becomes a conjunction of basic formulas of ML).

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© Springer Science+Business Media Dordrecht 1979