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Elementary pairs of primitive normal theories. (Russian, English) Zbl 1115.03029

Algebra Logika 43, No. 3, 321-340 (2004); translation in Algebra Logic 43, No. 3, 179-189 (2004).
Summary: The main objective of the paper is proving that classes of primitive normal, primitive bound, antiadditive, and additive theories are closed under \(P\)-expansions. This phenomenon is quite remarkable, for the main ‘structure’ classes of theories studied within model theory (such as stable, totally transcendental, etc.) do not possess such a property. Furthermore, it is proved that primitive bound theories are \(P\)-stable, and we furnish an example of a primitive bound theory with models that are not primitive bound.

MSC:

03C45 Classification theory, stability, and related concepts in model theory
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