We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Local Goldblatt—Thomason theorem.
- Authors
ZOLIN, EVGENY
- Abstract
The celebrated theorem proved by Goldblatt and Thomason in 1974 gives necessary and sufficient conditions for an elementary class of Kripke frames to be modally definable. Here we obtain a local analogue of this result, which deals with modal definability of classes of pointed frames. Furthermore, we generalize it to the case of n-frames, which are frames with n distinguished worlds. For talking about n-frames, we generalize modal formulas to modal expressions. While a modal formula is evaluated at a single world of a model, a modal expression with n individual variables is evaluated at an n-tuple of worlds, just as a first-order formula with n free variables. We introduce operations on n-frames that preserve validity of modal expressions, and show that closure under these operations is a necessary and sufficient condition for an elementary class of n-frames to be modally definable. We also discuss the relationship between modal expressions and hybrid logic and leave open questions.
- Subjects
MODAL logic; DEFINABILITY theory (Mathematical logic); MATHEMATICAL notation; EXPRESSION (Philosophy); FRAMES (Linguistics)
- Publication
Logic Journal of the IGPL, 2015, Vol 23, Issue 6, p861
- ISSN
1367-0751
- Publication type
Article
- DOI
10.1093/jigpal/jzv036