The theory of dual groups

ArticleOriginal scientific text

Title

Authors ¹, ¹

Department of Mathematics, University College of the Fraser Valley, 33844, King Rd., Abbotsford, British Columbia V2S 4N2, Canada

We study the

L_{\infty, w}

-theory of sequences of dual groups and give a complete classification of the

L_{\infty, w}

-elementary classes by finding simple invariants for them. We show that nonstandard models exist.

J. Barwise, Back and forth through infinitary logic, in: Studies in Model Theory, MAA Stud. Math. 8, Math. Assoc. Amer., 1973, 5-34.
S. Chase, Function topologies on abelian groups, Illinois J. Math. 7 (1963), 593-608.
K. Eda and H. Ohta, On abelian groups of integer-valued continuous functions, their ℤ-duals and ℤ-reflexivity, in: Abelian Group Theory, Proc. Third Conf. Oberwolfach, Gordon & Breach, 1987, 241-257.
P. Eklof and A. Mekler, Almost Free Modules, North-Holland, 1990.
P. Eklof, A. Mekler and S. Shelah, On strongly-non-reflexive groups, Israel J. Math. 59 (1987), 283-298.
E. Ellentuck, Categoricity regained, J. Symbolic Logic 41 (1976), 639-643.
G. Reid, Almost Free Abelian Groups, lecture notes, Tulane University, unpublished, 1968.
G. Schlitt, Sheaves of abelian groups and the quotients A**/A, J. Algebra 158 (1993), 50-60.

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