The Hart-Shelah example, in stronger logics

DOI10.1016/j.apal.2021.102958OpenAlexW3126734152MaRDI QIDQ2662698

Saharon Shelah, Andrés Villaveces

Publication date: 14 April 2021

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

Full work available at URL: https://arxiv.org/abs/math/0404258

zbMATH Keywords

model theoryinfinitary logiccategoricityabstract elementary classes

Mathematics Subject Classification ID

Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) (05C69) Other infinitary logic (03C75) Set-theoretic model theory (03C55) Categoricity and completeness of theories (03C35) Abstract elementary classes and related topics (03C48)

Cites Work

• Unnamed Item
• Categoricity over P for first order T or categoricity for \(\phi\) \(\in {\mathcal L}_{\omega_ 1\omega}\) can stop at \(\aleph_ k\) while holding for \(\aleph_ 0,\dots ,\aleph_{k-1}\)
• Classification theory for non-elementary classes. I: The number of uncountable models of \(\psi \in L_{\omega _ 1,\omega}\)
• Categoricity, amalgamation, and tameness
• Combinatorial set theory: Partition relations for cardinals
• Good frames in the Hart-Shelah example
• On the number of ${L}_{\infty \omega _1}$-equivalent non-isomorphic models
• Examples of non-locality
• Tameness and extending frames
• Large cardinal axioms from tameness in AECs
• Shelah's categoricity conjecture from a successor for tame abstract elementary classes
• GALOIS-STABILITY FOR TAME ABSTRACT ELEMENTARY CLASSES
• On strongly minimal sets

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