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23
Hyperimaginaries and Automorphism Groups
 Journal of Symbolic Logic
, 2000
"... this paper we are concerned with several issues: on the one hand, various levels of complexity of hyperimaginaries, and when hyperimaginaries can be reduced to simpler hyperimaginaries. On the other hand the issue of what information about hyperimaginaries in a saturated structure M can be obtained ..."
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Cited by 30 (11 self)
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this paper we are concerned with several issues: on the one hand, various levels of complexity of hyperimaginaries, and when hyperimaginaries can be reduced to simpler hyperimaginaries. On the other hand the issue of what information about hyperimaginaries in a saturated structure M can be obtained from the abstract group Aut(M ). In section 2 we show that if T is simple and canonical bases of Lascar strong types exist in M
A primer of simple theories
 Archive Math. Logic
"... Abstract. We present a selfcontained exposition of the basic aspects of simple theories while developing the fundamentals of forking calculus. We expound also the deeper aspects of S. Shelah’s 1980 paper Simple unstable theories. The concept of weak dividing has been replaced with that of forking. ..."
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Abstract. We present a selfcontained exposition of the basic aspects of simple theories while developing the fundamentals of forking calculus. We expound also the deeper aspects of S. Shelah’s 1980 paper Simple unstable theories. The concept of weak dividing has been replaced with that of forking. The exposition is from a contemporary perspective and takes into account contributions due to S. Buechler, E. Hrushovski, B. Kim, O. Lessmann, S. Shelah and A. Pillay.
On generically stable types in dependent theories
, 2007
"... Abstract. We develop the theory of generically stable types, independence relation based on nonforking and stable weight in the context of dependent (NIP) theories. ..."
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Cited by 11 (4 self)
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Abstract. We develop the theory of generically stable types, independence relation based on nonforking and stable weight in the context of dependent (NIP) theories.
From Stability To Simplicity
 Bulletin of Symbolic Logic 4
, 1998
"... this report we wish to describe recent work on a class of first order theories first introduced by Shelah in [32], the simple theories. Major progress was made in the first author's doctoral thesis [17]. We will give a survey of this, as well as further works by the authors and others. ..."
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Cited by 10 (2 self)
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this report we wish to describe recent work on a class of first order theories first introduced by Shelah in [32], the simple theories. Major progress was made in the first author's doctoral thesis [17]. We will give a survey of this, as well as further works by the authors and others.
Some remarks on indiscernible sequences
 Mathematical Logic Quarterly
"... We prove a property of generic homogeneity of tuples starting an infinite indiscernible sequence in a simple theory and we use it to give a shorter proof of the Independence Theorem for Lascar strong types. We also characterize the relation of starting an infinite indiscernible sequence in terms of ..."
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We prove a property of generic homogeneity of tuples starting an infinite indiscernible sequence in a simple theory and we use it to give a shorter proof of the Independence Theorem for Lascar strong types. We also characterize the relation of starting an infinite indiscernible sequence in terms of coheirs.
ORTHOGONALITY AND DOMINATION IN UNSTABLE THEORIES
"... Abstract. In the rst part of the paper we study orthogonality, domination, weight, regular and minimal types in the contexts of rosy and superrosy theories. Then we try to develop analogous theory for arbitrary dependent theories. 1. Introduction and ..."
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Abstract. In the rst part of the paper we study orthogonality, domination, weight, regular and minimal types in the contexts of rosy and superrosy theories. Then we try to develop analogous theory for arbitrary dependent theories. 1. Introduction and
A NOTE ON MORLEY SEQUENCES IN DEPENDENT THEORIES
"... Abstract. We characterize nonforking sequences in dependent (continuous and first order) theories in terms of a generalization of Poizat’s special sequences. We show that average types of Morley sequences are stationary over their domains and characterize generically stable types in terms of the str ..."
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Abstract. We characterize nonforking sequences in dependent (continuous and first order) theories in terms of a generalization of Poizat’s special sequences. We show that average types of Morley sequences are stationary over their domains and characterize generically stable types in terms of the structure of the “eventual ” type. 1.1. Introduction. To be added.
Stability of the theory of existentially closed Ssets over a right coherent monoid S’, wwwusers.york.ac.uk/∼varg1/2003paper.ps
"... Abstract. Let LS denote the language of (right) Ssets over a monoid S and let S be a set of sentences in LS which axiomatises Ssets. A general result of model theory says that S has a model companion, denoted by TS, precisely when the class E of existentially closed Ssets is axiomatisable and in ..."
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Abstract. Let LS denote the language of (right) Ssets over a monoid S and let S be a set of sentences in LS which axiomatises Ssets. A general result of model theory says that S has a model companion, denoted by TS, precisely when the class E of existentially closed Ssets is axiomatisable and in this case, TS axiomatises E. It is known that TS exists and is stable if and only if S is right coherent. In the study of stable first order theories, superstable and totally transcendental theories are of particular interest. We describe types over TS algebraically and use our result to confirm that TS is stable. We prove that TS is superstable if and only if S satisfies the maximal condition for right ideals. The situation for total transcendence is more complicated but a usable result is obtained for the case where Urank coincides with Morley rank. 1.