Ultrafilters and Independent Sets

DOI10.2307/1996350zbMath0263.02033OpenAlexW4251981819MaRDI QIDQ5678855

Kenneth Kunen

Publication date: 1973

Full work available at URL: https://doi.org/10.2307/1996350

Mathematics Subject Classification ID

Continuum hypothesis and Martin's axiom (03E50) Other combinatorial set theory (03E05) Other model constructions (03C30)

Related Items (54)

On projections of products of spaces ⋮ Cofinality spectrum theorems in model theory, set theory, and general topology ⋮ Partition Theorems and Ultrafilters ⋮ Ultrafilters, independent collections, and applications to topology ⋮ Countable ultraproducts without CH ⋮ Strong singularity, disjointness, and strong finite additivity of finitely additive measures ⋮ Keisler's order has infinitely many classes ⋮ Selctive ultrafilters and homogeneity ⋮ Independent Families in Complete Boolean Algebras ⋮ A Characterization and Sum Decomposition for Operator Ideals ⋮ Locally finite complexes, modules and generalized information systems ⋮ Closure index of semitopological groups ⋮ The Product of Two Countably Compact Topological Groups ⋮ Constructing regular ultrafilters from a model-theoretic point of view ⋮ Indestructibility properties of remarkable cardinals ⋮ Some simple theories from a Boolean algebra point of view ⋮ Open problems on ultrafilters and some connections to the continuum ⋮ Lower bounds of sets of P-points ⋮ Spaces homeomorphic to $\left( {2^\alpha } \right)_\alpha$ ⋮ Existence of optimal ultrafilters and the fundamental complexity of simple theories ⋮ On embedding certain partial orders into the P-points under Rudin-Keisler and Tukey reducibility ⋮ Independence of two set-theoretic statements in the theory of summation ⋮ Independence, order, and the interaction of ultrafilters and theories ⋮ Martin's axiom and pathological points in \(\beta\) X\(\backslash X\) ⋮ Kunen and set theory ⋮ Ken and \(\beta \mathbb N\) ⋮ The character spectrum of \(\beta \mathbb N\) ⋮ A dividing line within simple unstable theories ⋮ Hypergraph sequences as a tool for saturation of ultrapowers ⋮ Limits in the uniform ultrafilters ⋮ On the Rudin-Keisler order on ultrafilters ⋮ Some points in βN ⋮ An integer construction of infinitesimals: toward a theory of eudoxus hyperreals ⋮ GENERIC EXISTENCE OF MAD FAMILIES ⋮ Ultrafilters: Some old and some new results ⋮ Adequate Ultrafilters of Special Boolean Algebras ⋮ Refining families for ultrafilters ⋮ Partitions and Diamond ⋮ Realization of \(\varphi \)-types and Keisler's order ⋮ A homogeneous extremally disconnected countably compact space ⋮ Every two elementarily equivalent models have isomorphic ultrapowers ⋮ The Shelah P-point independence theorem ⋮ Quotient theorems via ultracoproducts ⋮ Néron desingularization of extensions of valuation rings (with an appendix by Kęstutis Česnavičius) ⋮ Unsolvability of several questions of convergence of series and sequences ⋮ On the product of homogeneous spaces ⋮ On the structure of generalized P-points ⋮ Orderings of ultrafilters on Boolean algebras ⋮ Many weak P-sets ⋮ On the cardinality and structure of extremally disconnected groups with linear topology ⋮ Nonregular Ultrafilters and Large Cardinals ⋮ Good and Ok Ultrafilters ⋮ Aggregating infinitely many probability measures ⋮ Pseudocompact refinements of compact group topologies

Cites Work

• Model theory
• Every two elementarily equivalent models have isomorphic ultrapowers
• Some theorems of set theory and their topological consequences
• Partial Orders on the Types in βN
• Boolean extensions and measurable cardinals
• Some applications of iterated ultrapowers in set theory

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