Boolean universes above Boolean models

Journal of Symbolic Logic 58 (4):1219-1250 (1993)
We establish several first- or second-order properties of models of first-order theories by considering their elements as atoms of a new universe of set theory and by extending naturally any structure of Boolean model on the atoms to the whole universe. For example, complete f-rings are "boundedly algebraically compact" in the language $(+,-,\cdot,\wedge,\vee,\leq)$ , and the positive cone of a complete l-group with infinity adjoined is algebraically compact in the language (+, ∨, ≤). We also give an example with any first-order language. The proofs can be translated into "naive set theory" in a uniform way
Keywords Atoms   Boolean models   first-order languages   convergence in lattice-ordered rings   equational compactness   algebraic compactness
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