No CrossRef data available.
Article contents
Theories of modules closed under direct products
Published online by Cambridge University Press: 12 March 2014
Abstract
We generalize to theories of modules (complete or not) a result of U. Felgner stating that a complete theory of abelian groups is a Horn theory if and only if it is closed under products. To prove this we show that a reduced product of modules ΠFMi (i ϵ I) is elementarily equivalent to a direct product of ultraproducts of the modules Mi(i ϵ I).
- Type
- Research Article
- Information
- Copyright
- Copyright © Association for Symbolic Logic 1992
References
REFERENCES
[1]Chang, C. C. and Keisler, H. J., Model theory, 3rd ed., North-Holland, Amsterdam, 1990.Google Scholar
[2]Felgner, U., Horn-theories of abelian groups, Model theory of algebra and arithmetic (Proceedings, Karpacz, 1979), Lectures Notes in Mathematics, vol. 834, Springer-Verlag, Berlin, 1980, pp. 163–173.CrossRefGoogle Scholar
[3]Galvin, F., Horn sentences, Annals of Mathematical Logic, vol. 1 (1970), pp. 389–422.CrossRefGoogle Scholar
[4]Keisler, H. J., Reduced products and Horn classes, Transactions of the American Mathematical Society, vol. 117 (1965), pp. 307–328.CrossRefGoogle Scholar
[5]Prest, M., Model theory and modules, London Mathematical Society Lecture Note Series, vol. 130, Cambridge University Press, Cambridge, 1988.CrossRefGoogle Scholar