Browsing by Author "Nurlanova A."

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    Expansion of models of DP-minimal theories
    (SDU University, 2025) Nurlanova A.
    This study investigates expansions of models of DP-minimal theories, a main subclass of dependent theories in model theory distinguished by well-controlled combinatorial complexity. Finding the circumstances in which DP-minimality is maintained when structures are extended by more predicates, functions, or relations is the main goal of the project. Following a thorough explanation of fundamental ideas like DP-rank, definability, and quantifier elimination, the study examines several extensions of the group of integers (Z, +, 0) and associated ordered algebraic systems. Expansions by linear orders and additional unary or binary predicates are important instances. The findings show that while some expansions lead to superstable but non-DPminimal expansions, others, like those corresponding to Presburger arithmetic (Z, +, <, 0, 1), preserve DP-minimality. By emphasizing the harmony between increased expressive power and minimality condition preservation, these results advance our knowledge of the relationship between model expansions and classification theory. The final section of the dissertation outlines possible avenues for future study, such as applications to ordered structures and broader classes of expansions.
  • Thumbnail Image
    ItemOpen Access
    Expansion of models of DP-minimal theories
    (SDU University, 2025) Nurlanova A.
    This study investigates expansions of models of DP-minimal theories, a main subclass of dependent theories in model theory distinguished by well-controlled combinatorial complexity. Finding the circumstances in which DP-minimality is maintained when structures are extended by more predicates, functions, or relations is the main goal of the project. Following a thorough explanation of fundamental ideas like DP-rank, definability, and quantifier elimination, the study examines several extensions of the group of integers (Z, +, 0) and associated ordered algebraic systems. Expansions by linear orders and additional unary or binary predicates are important instances. The findings show that while some expansions lead to superstable but non-DPminimal expansions, others, like those corresponding to Presburger arithmetic (Z, +, <, 0, 1), preserve DP-minimality. By emphasizing the harmony between increased expressive power and minimality condition preservation, these results advance our knowledge of the relationship between model expansions and classification theory. The final section of the dissertation outlines possible avenues for future study, such as applications to ordered structures and broader classes of expansions.