Algebra Univers. 78 (2017) 1–2
Published online May 24, 2017
© Springer International Publishing 2017
Bjarni J´onsson’s contributions in algebra: an addendum
Kirby A. Baker
Abstract. This note is an addendum to clarify credit for universal relational systems
and their properties.
The paper  requires ampliﬁcation in its account of the development of
the concept of a universal relational system and the associated conditions of
homogeneity and the amalgamation property. The discussion in [1, Section 2,
p. 309] might appear to suggest that these concepts originated with B. J´onsson
alone, but in actuality his papers  and  place these ideas in the context of
a line of precedents, parallels, and examples. In particular, for universal rela-
tional systems and homogeneity, J´onsson  cites earlier work of R. Fra¨ıss´e 
stemming from the countable case, while Fra¨ıss´e  in turn refers to a result of
Lindenbaum . In  J´onsson discusses the conditions used by Fra¨ıss´e [2, 4],
including amalgamation, and mentions then-new work of Vaught  and of
Morley, later appearing as . See also .
 Baker, K.A.: Bjarni J´onsson’s contributions in algebra. Algebra Universalis 31,
 Fra¨ıss´e, R.: Sur certaines relations qui g´en´eralisent l’ordre des nombres rationnels.
C. R. Acad. Sci. Paris 237, 540–542 (1953) (French)
 Fra¨ıss´e, R.: On certain relations which generalize ordering relations of type η. Bull.
Amer. Math. Soc. 59, 341–342 (1953)
 Fra¨ıss´e, R.: Sur l’extension aux relations de quelques propri´et´es des ordes. Ann. Sci.
Ecole Norm. Sup. 71, 363–388 (1954) (French)
 J´onsson, B.: Universal relational systems. Math. Scand. 4, 193–208 (1956)
 J´onsson, B.: Homogeneous universal relational systems. Math. Scand. 8, 137–142
 Lindenbaum, A.: Sur les bases des familles de fonctions. Annales de la Soci´et´e
Polonaise de Math´ematique 17, 124–126 (1938) (French)
 Morley, M., Vaught, R.: Homogeneous universal models. Math. Scand. 11, 37–57
 Vaught: R., Universal relational systems for elementary classes and types. Notices
Amer. Math.Soc. 5, 671 (1958)
Presented by G. Gratzer.
Received February 16, 2016; accepted in ﬁnal form February 20, 2016.
2010 Mathematics Subject Classiﬁcation: Primary: 03C52; Secondary: 03C05, 03C64.
Key words and phrases: universal relational system, homogeneous, amalgamation
The author is indebted to B. J´onsson for calling attention to the need for clariﬁcation
and to G. McNulty for valuable comments.