Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-16T16:10:55.952Z Has data issue: false hasContentIssue false

On properties of countable character

Published online by Cambridge University Press:  17 April 2009

Gabriel Sabbagh
Affiliation:
I, square Franςois Couperin, 92-Antony, France.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is proved that if a class X of algebras of countable similarity type is closed under isomorphism and ultrapower, then the class of subalgebras of direct products of elements of X is of countable character.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Barwise, J. and Eklof, P., “Infinitary properties of torsion abelian groups”, Ann. Math. Logic (to appear).Google Scholar
[2]Bell, J.L. and Slomson, A.B., Models and ultraproduots: an -introduction (North-Holland, Amsterdam, London, 1969)Google Scholar
[3]Cleave, John P., “Local properties of systems”, J. London Math. Soc. 44 (1969), 121130.CrossRefGoogle Scholar
[4]Cohn, P.M., Universal algebra, (Harper & Row, New York, Evanston, London, 1965).Google Scholar
[5]Eklof, P. and Sabbagh, Gabriel, “Definability problems for modules and rings”, submitted to J. Symbolic Logic.Google Scholar
[6]Kopperman, R.D. and Mathias, A.R.D., “Some problems in group theory”, The syntax and semantics of infinitary languages, 131138 (Lecture notes in Mathematics, 72, edited by Jon Barwise; Springer-Verlag, Berlin, Heidelberg, New York, 1968).CrossRefGoogle Scholar
[7]Neumann, B.H., “An embedding theorem for algebraic systems”, Proc. London Math. Soc. (3) 4 (1954), 138153.CrossRefGoogle Scholar
[8]Neumann, B.H., “Special topics in algebra: Universal algebra”, notes by Neumann, P.M., (Courant Institute of Mathematical Sciences, New York University, New York, 1962).Google Scholar
[9]Neumann, B.H., “Properties of countable character”, Proc. Internat. Congr. Math. (Nice, 1970), (to appear).Google Scholar
[10]Robinson, A., “Note on an embedding theorem for algebraic systems”, J. London Math. Soc. 30 (1955), 249252.CrossRefGoogle Scholar
[11]Sabbagh, Gabriel, “A note on the embedding property”, submitted to Math. Z.Google Scholar
[12]Tarski, Alfred, “Contributions to the theory of models. I”, Nederl. Akad. Wetensch. Proc. Ser. A. 57 (1954), 572581.CrossRefGoogle Scholar
[13]Tarski, Alfred and Vaught, Robert L., “Arithmetical extensions of relational systems”, Compositio Math. 13 (1957), 81102.Google Scholar
[14]Vaught, Robert, “The elementary character of two notions from general algebra”, Essays on the foundations of mathematics, 226233. (Magnes Press, Hebrew University, Jerusalem, 1961).Google Scholar
[15]Wenzel, G.H., “Compactness in algebraic structures”, (Report 68–31, Carnegie-Mellon University, Pittsburg, 1968).Google Scholar