Filtrations and Basic Proof Theory Notes for Lecture 5
نویسنده
چکیده
Note that !Σ is an equivalence relation. Let |w|Σ = {v | w !Σ v} denote the equivalence class of w under !Σ. Definition 1.1 (Filtration) Let M = 〈W,R, V 〉 be a Kripke model. Given a set of formulas closed under subformulas, a model Mf = 〈W f , Rf , V f 〉 is said to be a filtration of M through Σ provided • W f = {|w|Σ | w ∈W} • If wRv then |w|ΣR |v|Σ • If |w|ΣR |v|Σ then for each 3φ ∈ Σ, if M, v |= φ then M, w |= 3φ • V f (p) = {|w|Σ | w ∈ V (p)} /
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