Hypergraph sequences as a tool for saturation of ultrapowers

DOI10.2178/jsl/1327068699zbMath1247.03048OpenAlexW2037850209MaRDI QIDQ5388726

Maryanthe Malliaris

Publication date: 19 April 2012

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

Full work available at URL: https://projecteuclid.org/euclid.jsl/1327068699

zbMATH Keywords

ultrapowerregular ultrafiltercountable first-order theoriessequences of hypergraphsunstable classification

Mathematics Subject Classification ID

Hypergraphs (05C65) Ultraproducts and related constructions (03C20)

Related Items (18)

Cofinality spectrum theorems in model theory, set theory, and general topology ⋮ Cofinality spectrum problems: the axiomatic approach ⋮ On Kim-independence ⋮ Theories without the tree property of the second kind ⋮ Constructing regular ultrafilters from a model-theoretic point of view ⋮ Using ultrapowers to compare continuous structures ⋮ Some simple theories from a Boolean algebra point of view ⋮ Open problems on ultrafilters and some connections to the continuum ⋮ THE TURING DEGREES AND KEISLER’S ORDER ⋮ Existence of optimal ultrafilters and the fundamental complexity of simple theories ⋮ Independence, order, and the interaction of ultrafilters and theories ⋮ A dividing line within simple unstable theories ⋮ A new look at interpretability and saturation ⋮ An example of a new simple theory ⋮ Keisler's order is not simple (and simple theories may not be either) ⋮ Regularity lemmas for stable graphs ⋮ General topology meets model theory, on 𝔭 and 𝔱 ⋮ A separation theorem for simple theories

Cites Work

• Unnamed Item
• Unnamed Item
• Edge distribution and density in the characteristic sequence
• More on \(\mathrm{SOP}_1\) and \(\mathrm{SOP}_2\)
• Realization of \(\varphi \)-types and Keisler's order
• Classification theory and the number of non-isomorphic models.
• On \(\vartriangleleft^{*}\)-maximality.
• Toward classifying unstable theories
• Ultraproducts in the theory of models
• Limits in the uniform ultrafilters
• On uniform definability of types over finite sets
• The characteristic sequence of a first-order formula
• Simple unstable theories
• Lascar strong types in some simple theories
• Ultraproducts which are not saturated
• Ultrafilters and Independent Sets

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