Bjarni Jónsson and Alfred Tarski. Boolean algebras with operators. American journal of mathematics, vol. 73 (1951), pp. 891–939, and vol. 74 (1952), pp. 127–162.

1953 ◽  
Vol 18 (1) ◽  
pp. 70-71
Author(s):  
J. Richard Büchi
Keyword(s):  
Boolean Algebras ◽  
Boolean Algebras With Operators ◽  
Alfred Tarski

The contributions of Alfred Tarski to algebraic logic

1986 ◽  
Vol 51 (4) ◽  
pp. 899-906 ◽  
Author(s):  
J. Donald Monk
Keyword(s):  
Algebraic Logic ◽  
Boolean Algebras ◽  
Relation Algebras ◽  
Cylindric Algebras ◽  
Boolean Algebras With Operators ◽  
Alfred Tarski ◽  
The Subject ◽  
Closure Algebras

One of the most extensive parts of Tarski's contributions to logic is his work on the algebraization of the subject. His work here involves Boolean algebras, relation algebras, cylindric algebras, Boolean algebras with operators, Brouwerian algebras, and closure algebras. The last two are less developed in his work, although his contributions are basic to other work in those subjects. At any rate, not being conversant with the latest developments in those fields, we shall concentrate on an exposition of Tarski's work in the first four areas, trying to put them in the perspective of present-day developments.For useful comments, criticisms, and suggestions, the author is indebted to Steven Givant, Leon Henkin, Wilfrid Hodges, Bjarni Jónsson, Roger Lyndon, and Robert Vaught.

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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