On the existence of regular types

DOI10.1016/0168-0072(89)90039-0zbMath0697.03025OpenAlexW1991517235MaRDI QIDQ911582

Saharon Shelah, Steven Buechler

Publication date: 1989

Published in: Annals of Pure and Applied Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0168-0072(89)90039-0

zbMATH Keywords

prime modelsuperstable theoriesregular typesisolation relationNDOP

Mathematics Subject Classification ID

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

Related Items (7)

Unique decomposition in classifiable theories ⋮ Characterizing an \(\aleph_\varepsilon\)-saturated model of superstable NDOP theories by its \(\mathbb{L}_{\infty, \aleph_\varepsilon}\)-theory ⋮ Some remarks on nonmultidimensional superstable theories ⋮ Theories with few non-algebraic types over models, and their decompositions ⋮ Stability and omitting types ⋮ Classifiable theories without finitary invariants ⋮ A note on trivial nonmultidimensional superstable theories

Cites Work

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• The spectrum problem. I: \(\aleph_{\epsilon}\)-saturated models, the main gap
• A dichotomy theorem for regular types
• A survey of basic stability theory, with particular emphasis on orthogonality and regular types
• An exposition of Shelah's 'main gap': counting uncountable models of \(\omega\)-stable and superstable theories
• Dimensional order property and pairs of models
• On nontrivial types of U-rank 1
• Logic with the quantifier “there exist uncountably many”

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