Asymmetric regular types

[С. М. Моцоња]

110 листова

Математика - Математичка логика / Mathematics - Mathematical logic

У овом раду изучавамо асиметричне глобалне правилне типове. Ако је p правилан и асиметричан над А, тада постоји уређење такво да су Морлијеви низови у p над А строго растући. Испоставља се да за сваки мали модел...

In this thesis we study asymmetric regular types. If p is regular and asymmetric over A, then there exists an order such that Morley sequences in p over A are strictly increasing. It turns out that for every small model M  A, the order type of a maximal Morley sequence in p over A whose elements are from M does not depend on the choice of the sequence, i.e. it is an invariant of the model M denoted by Invp;A(M). In the countable case we can determine all possibilities for Invp;A(M): either Invp;A(M) is an arbitrary countable linear order or, provided that it contains at least two elements, it is a countable dense linear order (possibly with one or both endpoints). Also, we study the connection between Invp;A(M) and Invq;A(M), where p and q are two regular and asymmetric over A types such that pA 6?w qA. We distinguish two kinds of non-orthogonality: bounded and unbounded. Under the assumption that p and q are convex, in the bounded case we get that Invp;A(M) and Invq;A(M) are either isomorphic or anti-isomorphic, while under the assumption of strong regularity, in the unbounded case we get that Dedekind completions of Invp;A(M) and Invq;A(M) are either isomorphic or anti-isomorphic. In particular we study the following class of structures: expansions of linear orderings with countably many unary predicates and countably many equivalence relations with convex classes. We provide new examples of regular types. Namely, it turns out that every global invariant type in this context is regular, and every non-algebraic type over A has precisely two global extensions which are invariant over A. We also study the connection between the question of existence of a quasi- minimal model of a complete rst-order theory and the question of existence of a global strongly regular type. We also deal with the problem whether every quasi- minimal group must be abelian. It turns out that this question has the positive answer provided that the global extension of the generic type of a quasi-minimal group is asymmetric over...

глобалан тип, инваријантан тип, правилан тип, Морлијев низ, инваријанта, квазиминимална структура, линеарно уређење, оператор алге- барског затворења

global type, invariant type, regular type, Morley sequence, invariant, quasi-minimal structure, linear ordering, algebraic closure operator

510.67(043.3)

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