A survey of basic stability theory, with particular emphasis on orthogonality and regular types

DOI10.1007/BF02760649zbMath0583.03021OpenAlexW2061701929WikidataQ105836620 ScholiaQ105836620MaRDI QIDQ1069927

Michael Makkai

Publication date: 1984

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02760649

zbMATH Keywords

forkingorthogonal types

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45)

Related Items

Omitting types for stable ccc theories ⋮ Forking, normalization and canonical bases ⋮ Superstable quasi-varieties ⋮ Trivial pursuit: remarks on the main gap ⋮ Pseudoprojective strongly minimal sets are locally projective ⋮ \(\omega\)-stable structures of small CB-rank ⋮ S-homogeneity and automorphism groups ⋮ The notion of independence in categories of algebraic structures. I: Basic properties ⋮ Homogeneous models for unidimensional theories ⋮ On the number of nonisomorphic models of size |T| ⋮ Some remarks on nonmultidimensional superstable theories ⋮ Non-isolated types in stable theories ⋮ Dimensional order property and pairs of models ⋮ Simple, existentially closed extensions of unoids ⋮ A note on nonmultidimensional superstable theories ⋮ Classifying totally categorical groups (and others) ⋮ Stable theories, pseudoplanes and the number of countable models ⋮ Simple groups and the number of countable models ⋮ On nontrivial types of U-rank 1 ⋮ Imaginary modules ⋮ There is no sharp transitivity on q⁶ when q is a type of Morley rank 2 ⋮ CELLULAR CATEGORIES AND STABLE INDEPENDENCE ⋮ The independence relation in separably closed fields ⋮ On the number of models of uncountable theories ⋮ Constructing quasiminimal structures ⋮ ELIMINATION OF IMAGINARIES IN ORDERED ABELIAN GROUPS WITH BOUNDED REGULAR RANK ⋮ More on imaginaries in p-adic fields ⋮ Almost orthogonal regular types ⋮ A dichotomy theorem for regular types ⋮ On the existence of regular types ⋮ Characterization of \(\omega\)-stable theories of bounded dimension ⋮ A definable continuous rank for nonmultidimensional superstable theories ⋮ Non-totally transcendental unidimensional theories ⋮ Classification theory through stationary logic ⋮ Countable models of small stable theories ⋮ Forking independence from the categorical point of view ⋮ Locally finite weakly minimal theories ⋮ The classification of small weakly minimal sets. III: Modules ⋮ On homogeneous models of totally transcendental nonmultidimensional theories ⋮ Totally transcendental theories of unars ⋮ Classification and interpretation ⋮ Vaught's conjecture for superstable theories of finite rank ⋮ Kueker's conjecture for stable theories ⋮ On locally modular, weakly minimal theories ⋮ Coordinatization in Superstable Theories. I. Stationary Types ⋮ Structural problems for model companions of varieties of polygons ⋮ Countable models of superstable theories ⋮ Locally modular theories of finite rank ⋮ Weakly minimal formulas: A global approach ⋮ A Note on a-Prime Models ⋮ Coordinatisation and canonical bases in simple theories ⋮ Product of invariant types modulo domination-equivalence ⋮ Maximal hyperbolic towers and weight in the theory of free groups ⋮ On the elimination of imaginaries from certain valued fields ⋮ A note on trivial nonmultidimensional superstable theories ⋮ Vaught's conjecture for some meager groups ⋮ Unidimensional theories are superstable ⋮ Totally transcendental theories of modules: Decomposition of models and types ⋮ \({\mathcal M}\)-gap conjecture and \(m\)-normal theories ⋮ Coordinatization in Superstable Theories. II ⋮ Stability of weak second-order semantics ⋮ Finitely based theories ⋮ Borel completeness of some ℵ₀-stable theories ⋮ \mathbf P-NDOP and \mathbf P-decompositions of ℵ_ε-saturated models of superstable theories ⋮ Rings of finite representation type and modules of finite Morley rank ⋮ Ranks and pregeometries in finite diagrams ⋮ Resplendency and recursive definability in \(\omega\)-stable theories ⋮ A New Omitting Types Theorem ⋮ A proof of Vaught's conjecture for \(\omega\)-stable theories ⋮ First-order theories of abstract dependence relations ⋮ Invariants for \(\omega\)-categorical, \(\omega\)-stable theories ⋮ Однородность высокая и низкая

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