Cofinality spectrum theorems in model theory, set theory, and general topology

DOI10.1090/jams830zbMath1477.03125arXiv1208.5424OpenAlexW2087004834WikidataQ56689782 ScholiaQ56689782MaRDI QIDQ3450267

Saharon Shelah, Maryanthe Malliaris

Publication date: 3 November 2015

Published in: Journal of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.5424

Mathematics Subject Classification ID

Other combinatorial set theory (03E05) Cardinal characteristics of the continuum (03E17) Classification theory, stability, and related concepts in model theory (03C45) Ultraproducts and related constructions (03C20)

Related Items (35)

Preservation of splitting families and cardinal characteristics of the continuum ⋮ The linear refinement number and selection theory ⋮ Cofinality spectrum problems: the axiomatic approach ⋮ Towers and gaps at uncountable cardinals ⋮ Keisler's order has infinitely many classes ⋮ Subgroups of \(\mathrm{SF}(\omega)\) and the relation of almost containedness ⋮ Universal functions ⋮ The minimal size of infinite maximal antichains in direct products of partial orders ⋮ Model-theoretic applications of cofinality spectrum problems ⋮ Constructing regular ultrafilters from a model-theoretic point of view ⋮ Atomic saturation of reduced powers ⋮ On cuts in ultraproducts of linear orders I ⋮ 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 ⋮ Splitting positive sets ⋮ Generalised pseudointersections ⋮ Forcing and the universe of sets: must we lose insight? ⋮ A large list of small cardinal characteristics of Boolean algebras ⋮ THE TURING DEGREES AND KEISLER’S ORDER ⋮ Existence of optimal ultrafilters and the fundamental complexity of simple theories ⋮ A characterization of the Boolean Prime Ideal theorem in terms of forcing notions ⋮ A dividing line within simple unstable theories ⋮ A new look at interpretability and saturation ⋮ ON CUTS IN ULTRAPRODUCTS OF LINEAR ORDERS II ⋮ Keisler's order is not simple (and simple theories may not be either) ⋮ Controlling cardinal characteristics without adding reals ⋮ A parallel to the null ideal for inaccessible \(\lambda\). I ⋮ Base tree property ⋮ Construction with opposition: cardinal invariants and games ⋮ Selective covering properties of product spaces, II: $\gamma $ spaces ⋮ Small cardinals and the pseudocompactness of hyperspaces of subspaces of \(\beta\omega\) ⋮ TOWERS IN FILTERS, CARDINAL INVARIANTS, AND LUZIN TYPE FAMILIES ⋮ Questions on generalised Baire spaces ⋮ Ramsey degrees of ultrafilters, pseudointersection numbers, and the tools of topological Ramsey spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cofinality spectrum problems: the axiomatic approach
• Independence, order, and the interaction of ultrafilters and theories
• Existence of optimal ultrafilters and the fundamental complexity of simple theories
• More on \(\mathrm{SOP}_1\) and \(\mathrm{SOP}_2\)
• Realization of \(\varphi \)-types and Keisler's order
• On the scheme of induction for bounded arithmetic formulas
• Classification theory and the number of non-isomorphic models.
• Classification theory and the number of non-isomorphic models
• On \(\vartriangleleft^{*}\)-maximality.
• Keisler's order has infinitely many classes
• Two cardinal invariants of the continuum \(({\mathfrak d} <{\mathfrak a})\) and FS linearly ordered iterated forcing
• Asymptotic cones of finitely presented groups
• Toward classifying unstable theories
• Ultraproducts in the theory of models
• Model-theoretic applications of cofinality spectrum problems
• A dividing line within simple unstable theories
• Good ideals in fields of sets
• The elementary theory of finite fields
• Every two elementarily equivalent models have isomorphic ultrapowers
• MODEL-THEORETIC PROPERTIES OF ULTRAFILTERS BUILT BY INDEPENDENT FAMILIES OF FUNCTIONS
• Constructing regular ultrafilters from a model-theoretic point of view
• Coherent Sequences
• Combinatorial Cardinal Characteristics of the Continuum
• Good and Ok Ultrafilters
• A Comment on “ 𝔭 < t”
• The space of ultrafilters on N covered by nowhere dense sets
• On the combinatorial principle P(c)
• Some Remarks on Category in Topological Spaces
• Simple unstable theories
• Cardinalities of ultraproducts of finite sets
• Hypergraph sequences as a tool for saturation of ultrapowers
• Diophantine Problems Over Local Fields I
• Ultraproducts which are not saturated
• Ultrafilters and Independent Sets
• On some problems of Hausdorff and of Sierpiński

This page was built for publication: Cofinality spectrum theorems in model theory, set theory, and general topology