Existence of many \(L_{\infty,\lambda}\)-equivalent, non-isomorphic models of T of power \(\lambda\)

DOI10.1016/0168-0072(87)90005-4zbMath0624.03030OpenAlexW2024445326MaRDI QIDQ1092040

Saharon Shelah

Publication date: 1987

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(87)90005-4

zbMATH Keywords

superstable theoryabelian p-groupsinfinitary languagedopgeneralized EM- modelsotop

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Other infinitary logic (03C75)

Related Items (12)

Universal theories categorical in power and \(\kappa\)-generated models ⋮ Characterizing an \(\aleph_\varepsilon\)-saturated model of superstable NDOP theories by its \(\mathbb{L}_{\infty, \aleph_\varepsilon}\)-theory ⋮ Potential isomorphism of elementary substructures of a strictly stable homogeneous model ⋮ The theorems of Beth and Craig in abstract model theory. III: \(\Delta\)- logics and infinitary logics ⋮ Constructing strongly equivalent nonisomorphic models for unstable theories ⋮ A combinatorial principle and endomorphism rings. I: On \(p\)-groups ⋮ Two cardinal invariants of the continuum \(({\mathfrak d} <{\mathfrak a})\) and FS linearly ordered iterated forcing ⋮ Generalized Descriptive Set Theory and Classification Theory ⋮ A descriptive Main Gap Theorem ⋮ Borel completeness of some ℵ₀-stable theories ⋮ Categoricity for abstract classes with amalgamation ⋮ Toward categoricity for classes with no maximal models

Cites Work

• Constructions of many complicated uncountable structures and Boolean algebras
• A pair of nonisomorphic \(\equiv _{\infty \lambda}\) models of power \(\lambda\) for \(\lambda\) singular with \(\lambda ^{\omega}=\lambda\)
• Around classification theory of models
• Better quasi-orders for uncountable cardinals
• Infinite Abelian groups, Whitehead problem and some constructions
• Classification theory and the number of non-isomorphic models
• On Fraissé's order type conjecture
• L ∞λ -Equivalence, Isomorphism and Potential Isomorphism

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