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Results on Boolean algebras with applications to the model theory of l-groups
by
Brian Wynne
Bard College at Simon's Rock
In [1] Tarski gives numerical invariants that classify Boolean algebras with respect to elementary equivalence and yield the decidability of the theory of Boolean algebras. In [3] Weispfenning obtains invariants and decidability for certain l-groups by reducing their theory to that of Boolean algebras. We discuss analogous results for a different but related class of l-groups of the form C(X) with X an essential P-space. The theory of such an l-group may often be reduced to that of an associated Boolean algebra with distinguished ideal. Using work of Touraille [2] we obtain invariants and decidability for some of these associated structures and hence for the corresponding l-groups.
References:
[1] A. Tarski, Arithmetical classes and types of Boolean algebras, Bulletin of the American Mathematical Society 55 (1949), 64.
[2] A. Touraille, Théories d'algèbres de Boole munies d'idéaux distingués. I. Théories élémentaires, The Journal of Symbolic Logic 52 (1987), no. 4, 1027-1043.
[3] V. Weispfenning, Model Theory Of Abelian l-Groups, in: A.M.W. Glass and W.C. Holland, editors, Lattice-ordered groups, Kluwer Academic Press, Dordrecht (1989), 41-79.
Date received: May 26, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxi-12.