 Author
 Year
 2013
 Title
 CRS and Guarded Logics: a fruitful contact
 Book title
 Cylindriclike algebras and algebraic logic
 Pages (fromto)
 273301
 Publisher
 Budapest: Springer
 ISBN
 9783642350252
 Serie
 Bolyai Society Mathematical Studies
 Volume  Edition (Serie)
 22
 Document type
 Chapter
 Faculty
 Interfacultary Research Institutes
 Institute
 Institute for Logic, Language and Computation (ILLC)
 Abstract

Back and forth between algebra and model theory. Algebra and model theory are complementary stances in the history of logic, and their interaction continues to spawn new ideas, witness the interface of FirstOrder Logic and Cylindric Algebra. This chapter is about a more specialized contact: the flow of ideas between algebra and modal logic through ‘guarded fragments’ restricting the range of quantification over objects. Here is some general background for this topic. For a start, the connection between algebra and model theory is rather tight, since we can view universal algebra as the equational logic part of standard firstorder model theory. As an illustration, van Benthem [Ben,88] has a purely modeltheoretic proof of Jónsson’s Theorem characterizing the equational varieties with distributive lattices of congruence relations, a major tool of algebraists. Deeper connections arise in concrete cases with categorial dualities, such as that between BAOs and the usual relational models of modal logic. An important example is the main theorem in Goldblatt and Thomason [GolTho,74] characterizing the elementary modally definable frame classes through their closure under taking generated subframes, disjoint unions, pmorphic images, and anticlosure under ultrafilter extensions. Its original proof goes back and forth between algebras and frames, in order to apply Birkhoff’s characterization of equational varieties.
 URL
 go to publisher's site
 Language
 English
 Permalink
 http://hdl.handle.net/11245/1.381628
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