scholarly journals The preservation of Sahlqvist equations in completions of Boolean algebras with operators

1999 ◽  
Vol 41 (1) ◽  
pp. 47-84 ◽  
Author(s):  
S. Givant ◽  
Y. Venema
Keyword(s):  
Boolean Algebras ◽  
Boolean Algebras With Operators

Boolean Algebras with Operators

1952 ◽  
Vol 74 (1) ◽  
pp. 127 ◽  
Author(s):  
Bjarni Jonnson ◽  
Alfred Tarski
Keyword(s):  
Boolean Algebras ◽  
Boolean Algebras With Operators

Amalgamation in relation algebras

1998 ◽  
Vol 63 (2) ◽  
pp. 479-484 ◽  
Author(s):  
Maarten Marx
Keyword(s):  
Modal Logic ◽  
Equational Theory ◽  
Weak Form ◽  
Boolean Algebras ◽  
The Other ◽  
Relation Algebras ◽  
Boolean Algebras With Operators ◽  
Other Hand ◽  
Arrow Logic ◽  
Representable Relation

We investigate amalgamation properties of relational type algebras. Besides purely algebraic interest, amalgamation in a class of algebras is important because it leads to interpolation results for the logic corresponding to that class (cf. [15]). The multi-modal logic corresponding to relational type algebras became known under the name of “arrow logic” (cf. [18, 17]), and has been studied rather extensively lately (cf. [10]). Our research was inspired by the following result of Andréka et al. [1].Let K be a class of relational type algebras such that(i) composition is associative,(ii) K is a class of boolean algebras with operators, and(iii) K contains the representable relation algebras RRA.Then the equational theory of K is undecidable.On the other hand, there are several classes of relational type algebras (e.g., NA, WA denned below) whose equational (even universal) theories are decidable (cf. [13]). Composition is not associative in these classes. Theorem 5 indicates that also with respect to amalgamation (a very weak form of) associativity forms a borderline. We first recall the relevant definitions.

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