Upward categoricity from a successor cardinal for tame abstract classes with amalgamation

DOI10.2178/jsl/1120224733zbMath1089.03025OpenAlexW2050580270MaRDI QIDQ5718680

Olivier Lessmann

Publication date: 16 January 2006

Published in: Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2178/jsl/1120224733

zbMATH Keywords

amalgamationsuccessor cardinaltame abstract elementary classupward categoricity theorem

Mathematics Subject Classification ID

Set-theoretic model theory (03C55) Categoricity and completeness of theories (03C35)

Related Items (10)

CATEGORICITY FROM ONE SUCCESSOR CARDINAL IN TAME ABSTRACT ELEMENTARY CLASSES ⋮ Categoricity, amalgamation, and tameness ⋮ Categoricity transfer in simple finitary abstract elementary classes ⋮ Abstract elementary classes stable in \(\aleph_{0}\) ⋮ Shelah's eventual categoricity conjecture in tame abstract elementary classes with primes ⋮ Uncountable categoricity of local abstract elementary classes with amalgamation ⋮ Tameness and extending frames ⋮ Shelah's categoricity conjecture from a successor for tame abstract elementary classes ⋮ Uniqueness of limit models in classes with amalgamation ⋮ Uncountably categorical local tame abstract elementary classes with disjoint amalgamation

Cites Work

• Classification theory for non-elementary classes. I: The number of uncountable models of \(\psi \in L_{\omega _ 1,\omega}\)
• Toward categoricity for classes with no maximal models
• Amalgamation properties and finite models in \(L^n\)-theories
• Almost free algebras
• Finite diagrams stable in power
• Categoricity of an abstract elementary class in two successive cardinals

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