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Stability and Morley rank
 Hrushovski’s Proof of the Geometric MordellLang Conjecture, number 1696 in Lecture Notes in Mathematics
, 1998
"... Let f: D → E be a definable map between definable classes. The following theorem is well known: Theorem 1 ([1], [2, V 6.8]) If E has Morley rank β and the Morley rank of all fibers f −1 (e) is bounded by α. Then ..."
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Let f: D → E be a definable map between definable classes. The following theorem is well known: Theorem 1 ([1], [2, V 6.8]) If E has Morley rank β and the Morley rank of all fibers f −1 (e) is bounded by α. Then
MORLEY RANK IN HOMOGENEOUS MODELS
"... Abstract. We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α, then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct Dextensions of rank α. This is surprising, because the proof of the statem ..."
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Abstract. We define an appropriate analog of the Morley rank in a totally transcendental homogeneous model with type diagram D. We show that if RM[p] = α, then for some 1 ≤ n < ω the type p has n, but not n + 1, distinct Dextensions of rank α. This is surprising, because the proof
Linear groups of finite Morley rank
, 2008
"... Zilber’s original trichotomy conjecture proposed an explicit classification of all onedimensional objects arising in model theory. At one point, classifying the simple groups of finite Morley rank was viewed as a subproblem whose affirmative ..."
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Zilber’s original trichotomy conjecture proposed an explicit classification of all onedimensional objects arising in model theory. At one point, classifying the simple groups of finite Morley rank was viewed as a subproblem whose affirmative
The Morley rank of a Banach space
, 1996
"... . We introduce the concepts of Morley rank and Morley degree for structures based on Banach spaces. We characterize !stability in terms of Morley rank, and prove the existence of prime models for !stable theories. 1. introduction A general framework for the model theoretical analysis of structure ..."
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. We introduce the concepts of Morley rank and Morley degree for structures based on Banach spaces. We characterize !stability in terms of Morley rank, and prove the existence of prime models for !stable theories. 1. introduction A general framework for the model theoretical analysis
A generation theorem for groups of finite Morley rank
 In preparation (draft available
, 2008
"... Groups of finite Morley rank A group of finite Morley rank is a group equipped with a notion of dimension satisfying various natural axioms [BN94, p. 57]; These groups arise naturally in model theory, expecially geometrical stability theory. The main examples are ..."
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Groups of finite Morley rank A group of finite Morley rank is a group equipped with a notion of dimension satisfying various natural axioms [BN94, p. 57]; These groups arise naturally in model theory, expecially geometrical stability theory. The main examples are
Small groups of finite Morley rank with involutions
 J. Reine Angew. Math
"... By analogy with Thompson’s classification of nonsolvable finite Ngroups, we classify groups of finite Morley rank with solvable local subgroups of even and of mixed type. We also consider miscellaneous aspects concerning “small ” groups of finite Morley rank of odd type. 1 ..."
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By analogy with Thompson’s classification of nonsolvable finite Ngroups, we classify groups of finite Morley rank with solvable local subgroups of even and of mixed type. We also consider miscellaneous aspects concerning “small ” groups of finite Morley rank of odd type. 1
Lascar and Morley ranks differ in differentially closed fields
 Journal of Symbolic Logic
, 1999
"... We note here, in answer to a question of Poizat, that the Morley and Lascar ranks need not coincide in differentially closed fields. We will approach this through the (perhaps) more fundamental issue of the variation of Morley rank in families. We will be interested here only in sets of finite Morle ..."
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We note here, in answer to a question of Poizat, that the Morley and Lascar ranks need not coincide in differentially closed fields. We will approach this through the (perhaps) more fundamental issue of the variation of Morley rank in families. We will be interested here only in sets of finite
LINEAR REPRESENTATIONS OF SOLUBLE GROUPS OF FINITE MORLEY RANK
"... Abstract. Sufficient conditions are given for groups of finite Morley rank having nontrivial torsionfree nilpotent normal subgroups to have linear representations with small kernels. In particular, centreless connected soluble groups of finite Morley rank with torsionfree Fitting subgroups have f ..."
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Abstract. Sufficient conditions are given for groups of finite Morley rank having nontrivial torsionfree nilpotent normal subgroups to have linear representations with small kernels. In particular, centreless connected soluble groups of finite Morley rank with torsionfree Fitting subgroups have
K*Groups of Finite Morley rank and of even type
, 1999
"... An infinite simple K # group of finite Morley rank of even type is a Chevalley group over an algebraically closed field of characteristic 2. Proposed draft. The supporting results are not complete at this time. ..."
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An infinite simple K # group of finite Morley rank of even type is a Chevalley group over an algebraically closed field of characteristic 2. Proposed draft. The supporting results are not complete at this time.
The Bender method in groups of finite Morley rank
, 2008
"... The algebraicity conjecture for simple groups of finite Morley rank, also known as the CherlinZilber conjecture, states that simple groups of finite Morley rank are simple algebraic groups over algebraically closed fields. In the last 15 years, the main line of attack on this problem has been Borov ..."
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The algebraicity conjecture for simple groups of finite Morley rank, also known as the CherlinZilber conjecture, states that simple groups of finite Morley rank are simple algebraic groups over algebraically closed fields. In the last 15 years, the main line of attack on this problem has been
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