More on \(\mathrm{SOP}_1\) and \(\mathrm{SOP}_2\)

DOI10.1016/j.apal.2008.02.003zbMath1154.03015arXivmath/0404178OpenAlexW2152317143MaRDI QIDQ947266

Alexander Usvyatsov, Saharon Shelah

Publication date: 29 September 2008

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

Full work available at URL: https://arxiv.org/abs/math/0404178

zbMATH Keywords

rank\(\triangleleft^*\)-maximalityKeisler orderingSOP\(_{1}\)SOP\(_{2}\)

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Properties of classes of models (03C52) Abstract model theory (03C95)

Related Items (18)

Cofinality spectrum theorems in model theory, set theory, and general topology ⋮ Generic expansion and Skolemization in \(\mathrm{NSOP}_{1}\) theories ⋮ Cofinality spectrum problems: the axiomatic approach ⋮ Model-theoretic applications of cofinality spectrum problems ⋮ On Kim-independence ⋮ Constructing regular ultrafilters from a model-theoretic point of view ⋮ Atomic saturation of reduced powers ⋮ \(\mathrm{SOP}_1\), \(\mathrm{SOP}_2\), and antichain tree property ⋮ Edge distribution and density in the characteristic sequence ⋮ Notions around tree property 1 ⋮ Universality: new criterion for non-existence ⋮ Independence, order, and the interaction of ultrafilters and theories ⋮ A dividing line within simple unstable theories ⋮ Hypergraph sequences as a tool for saturation of ultrapowers ⋮ A new look at interpretability and saturation ⋮ Generic expansions by a reduct ⋮ Dense codense predicates and the NTP₂ ⋮ The characteristic sequence of a first-order formula

Cites Work

• Unnamed Item
• Classification theory and the number of non-isomorphic models.
• On \(\vartriangleleft^{*}\)-maximality.
• Toward classifying unstable theories

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