Browsing by Author "Rassayeva N."

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    Conservative extensions of NIP non dp-minimal theories
    (SDU University, 2025) Rassayeva N.
    This dissertation explores conservative extensions in the context of dependent theories (NIP) that are not dp-minimal. We study the model-theoretic properties of the special Cartesian product of ordered structures, focusing on how the dprank and definability of types behave under such constructions. It is shown that the product of two o-minimal or two weakly o-minimal structures yields a theory of dp-rank 2, which remains NIP but is no longer dp-minimal. Further, we analyze the behavior of 1-conservative and n-conservative extensions in these theories. For o-minimal structures, 1-conservativity implies nconservativity for all finite n, ensuring strong definability of types. However, for weakly o-minimal structures, this implication fails; we construct an explicit example where a 1-conservative extension does not extend to a 2-conservative one. The results provide new insights into how model-theoretic complexity measured by dp-rank affects definability and extendability in NIP theories, contributing to the classification and understanding of dependent but non-dp-minimal structures.