General topology meets model theory, on 𝔭 and 𝔱

DOI10.1073/pnas.1306114110zbMath1301.03041OpenAlexW2016460164WikidataQ37103918 ScholiaQ37103918MaRDI QIDQ5170971

Saharon Shelah, Maryanthe Malliaris

Publication date: 25 July 2014

Published in: Proceedings of the National Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1073/pnas.1306114110

zbMATH Keywords

ultrapowerscardinal invariants of the continuumKeisler's order

Mathematics Subject Classification ID

Cardinal characteristics of the continuum (03E17) Classification theory, stability, and related concepts in model theory (03C45) Ultraproducts and related constructions (03C20)

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Cites Work

• Independence, order, and the interaction of ultrafilters and theories
• Edge distribution and density in the characteristic sequence
• Realization of \(\varphi \)-types and Keisler's order
• Two cardinal invariants of the continuum \(({\mathfrak d} <{\mathfrak a})\) and FS linearly ordered iterated forcing
• Toward classifying unstable theories
• Good ideals in fields of sets
• A Comment on “ 𝔭 < t”
• Hypergraph sequences as a tool for saturation of ultrapowers
• Ultraproducts which are not saturated
• THE INDEPENDENCE OF THE CONTINUUM HYPOTHESIS
• On strongly minimal sets
• Short complete nested sequences in βN⧹N and small maximal almost-disjoint families
• Consistency-Proof for the Generalized Continuum-Hypothesis