caa a22 4500 388039221 CHVBK 20180307125016.0 cr unu---uuuuu 161130e199806 xx s 000 0 eng 10.2307/2586844 doi S0022481200015024 pii (NATIONALLICENCE)cambridge-10.2307/2586844 Marx Maarten Department of Computing, Imperial College, 180 Queen's Gate, SW7 2BZ London, UK, E-mail: m.marx@doc.ic.ac.uk Amalgamation in relation algebras [Elektronische Daten] [Maarten Marx] 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. Copyright © Association for Symbolic Logic 1998 The Journal of Symbolic Logic Cambridge University Press 63/2(1998-06), 479-484 0022-4812 63:2<479 1998 63 JSL https://doi.org/10.2307/2586844 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586844 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Marx Maarten Department of Computing, Imperial College, 180 Queen's Gate, SW7 2BZ London, UK, E-mail: m.marx@doc.ic.ac.uk NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/2(1998-06), 479-484 0022-4812 63:2<479 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge