Generic expansion and Skolemization in \(\mathrm{NSOP}_{1}\) theories

DOI10.1016/j.apal.2018.04.003zbMath1469.03096arXiv1706.06616OpenAlexW2720779990WikidataQ129741656 ScholiaQ129741656MaRDI QIDQ2636528

Nicholas Ramsey, Alex Kruckman

Publication date: 5 June 2018

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

Full work available at URL: https://arxiv.org/abs/1706.06616

zbMATH Keywords

expansionsSkolem functionsgeneric structures\(\mathrm{NSOP}_1\)

Mathematics Subject Classification ID

Classification theory, stability, and related concepts in model theory (03C45) Quantifier elimination, model completeness, and related topics (03C10)

Related Items (14)

Pathological examples of structures with o‐minimal open core ⋮ Generic expansion of an abelian variety by a subgroup ⋮ Companionability characterization for the expansion of an o-minimal theory by a dense subgroup ⋮ TRANSITIVITY, LOWNESS, AND RANKS IN NSOP THEORIES ⋮ \(\mathrm{SOP}_1\), \(\mathrm{SOP}_2\), and antichain tree property ⋮ Recursive functions and existentially closed structures ⋮ Universality: new criterion for non-existence ⋮ Transitivity of Kim-independence ⋮ Interpolative fusions ⋮ FORKING, IMAGINARIES, AND OTHER FEATURES OF ⋮ Generic expansions by a reduct ⋮ INDEPENDENCE IN GENERIC INCIDENCE STRUCTURES ⋮ Independence over arbitrary sets in \(\mathrm{NSOP}_1\) theories ⋮ WEAK CANONICAL BASES IN NSOP THEORIES

Cites Work

• Theories without the tree property of the second kind
• Adding Skolem functions to simple theories
• More on \(\mathrm{SOP}_1\) and \(\mathrm{SOP}_2\)
• Model theory.
• Generic structures and simple theories
• On \(\vartriangleleft^{*}\)-maximality.
• Forking and dividing in Henson graphs
• On model-theoretic tree properties
• A GEOMETRIC INTRODUCTION TO FORKING AND THORN-FORKING
• Local character of Kim-independence
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