filtration
Let be a Kripke model for a modal logic . Let be a set of wff’s. Define a binary relation on :
Then is an equivalence relation on . Let be the set of equivalence classes of on . It is easy to see that if is finite, so is . Next, let
Then is a well-defined function. We call a binary relation on a filtration of if
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•
implies
-
•
implies that for any wff with , if , then .
The triple is called a filtration of the model .
Proposition 1.
(Filtration Lemma) Let be a set of wff’s closed under the formation of subformulas: any subformula of any formula in is again in . Then
Title | filtration |
---|---|
Canonical name | Filtration1 |
Date of creation | 2013-03-22 19:35:39 |
Last modified on | 2013-03-22 19:35:39 |
Owner | CWoo (3771) |
Last modified by | CWoo (3771) |
Numerical id | 8 |
Author | CWoo (3771) |
Entry type | Definition |
Classification | msc 03B45 |
\@unrecurse |