Decidable theories of non-projectable l-groups of continuous functions

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Abstract

We study the class of l-groups of the form C(X) with X an essential P-space. Many such l-groups are non-projectable and their elementary theories may often be reduced to that of an associated Boolean algebra with distinguished ideal. In this paper we establish the decidability of the theories of two classes of such l-groups via corresponding results for the associated structures.

Keywords

Decidable theory
l-group
P-space
Boolean algebra

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This paper is a revision of the author’s doctoral dissertation, written under the direction of Philip Scowcroft at Wesleyan University. The author would like to thank Dr Scowcroft for his guidance and for helpful comments on earlier versions of this paper.