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Elementary Pairs of Primitive Normal Theories
Authors:E A Palyutin
Institution:(1) Institute of Mathematics SB RAS, Akademika Koptyuga Prospekt, 4, Novosibirsk, 630090, Russia
Abstract: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 ldquostructurerdquo 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.
Keywords:elementary pairs  primitive normal theory  primitive bound theory  antiadditive theory  additive theory  primitive bound model
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