Abstract
The paper is a survey of results in the model theory of abelian groups, dealing with two sorts of problems: finding invariants which classify groups up toL λκ-equivalence; and determining whether certain classes of groups are definable inL λκ.
Similar content being viewed by others
References
J. Barwise,Back and forth through infinitary, logic, inStudies in Model Theory, MAA Studies in Mathematics, Vol. 8 (M. Morley, ed.), Math. Assoc. of Amer, 1973, pp. 5–34.
J. Barwise and P. Eklof,Infinitary properties of abelian torsion groups, Ann. Math. Logic2 (1970), 25–68.
M. Benda,Reduced products and non-standard logics, J. Symbolic Logic34 (1969), 424–436.
J. P. Calais,La méthode de Fraissé dans les languages infininis, C. R. Acad. Sci. Paris A268 (1969), 785–788.
P. Eklof,Infinitary equivalence of abelian groups, Fund. Math81 (1974), 305–314.
P. Eklof,On the existence of κ-free abelian groups, Proc. Amer Math. Soc.47 (1975), 65–72.
P. Eklof,Homological algebra and set theory, to appear in Trans. Amer. Math. Soc.
P. Eklof and E. Fisher,The elementary theory of abelian groups, Ann. Math. Logic4 (1972), 115–171.
L. Fuchs,Infinite Abelian Groups, Vol. I, Academic Press, New York, 1970.
L. Fuchs,Infinite Abelian Groups, Vol. II, Academic Press, New York, 1973.
J. Gregory,Abelian groups infinitarily equivalent to free ones, Notices Amer. Math. Soc.20 (1973), A-500.
D. Kueker,Countable approximations and Lowenheim-Skolem theorems, preprint.
C. Megibben,On mixed groups of torsion-free rank one, Illinois J. Math.,11 (1967), 134–144.
A. Mekler, Ph.D. Dissertation, Stanford University, 1976.
S. Shelah,Infinite abelian groups, Whitehead problem and some constructions, Israel J. Math.18 (1974), 243–256.
S. Shelah,A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals, Israel J. Math.21 (1975), 319–349.
W. Szmielew,Elementary properties of abelian groups, Fund. Math.41 (1955), 203–271.
Author information
Authors and Affiliations
Additional information
Research supported by NSF grant GP 43910
Rights and permissions
About this article
Cite this article
Eklof, P.C. Infinitary model theory of abelian groups. Israel J. Math. 25, 97–107 (1976). https://doi.org/10.1007/BF02756564
Issue Date:
DOI: https://doi.org/10.1007/BF02756564