Ideals over uncountable sets: application of almost disjoint functions and generic ultrapowers

DOI10.1090/memo/0214zbMath0398.03044OpenAlexW2031001261MaRDI QIDQ4182742

Karel Prikry, Thomas J. Jech

Publication date: 1979

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

Full work available at URL: https://doi.org/10.1090/memo/0214

zbMATH Keywords

forcingmeasurable cardinaluncountable setscombinatorial set theorygeneralized continuum hypothesissaturation of idealsgeneric ultrapowersnormal ultrafiltersingular cardinals problemalmost disjoint functions

Mathematics Subject Classification ID

Large cardinals (03E55) Cardinality properties (cardinal functions and inequalities, discrete subsets) (54A25) Continuum hypothesis and Martin's axiom (03E50) Other combinatorial set theory (03E05) Ultraproducts and related constructions (03C20) Other aspects of forcing and Boolean-valued models (03E40)

Related Items (22)

Menas' conjecture and generic ultrapowers ⋮ A hierarchy of Ramsey cardinals ⋮ More on powers of singular cardinals ⋮ Cardinal arithmetic for skeptics ⋮ A characterization of cardinals \(\kappa\) such that \(2^{\lambda}=2^{\kappa}\) whenever \(\kappa \leq \lambda <2^{\kappa}\) ⋮ Exact functors, local connectedness and measurable cardinals ⋮ The higher Cichoń diagram in the degenerate case ⋮ Saturated ideals and the singular cardinal hypothesis ⋮ Iterated forcing and changing cofinalities ⋮ Saturation Properties of Ideals in Generic Extensions. I ⋮ A hierarchy of filters on regular uncountable cardinals ⋮ More on regular and decomposable ultrafilters in ZFC ⋮ Measurable cardinals and the cardinality of Lindelöf spaces ⋮ A new characterization of supercompactness and applications ⋮ The saturation of club guessing ideals ⋮ Some examples of precipitous ideals ⋮ Completion of Factor Algebras of Ideals ⋮ WEAK REFLECTION PRINCIPLE, SATURATION OF THE NONSTATIONARY IDEAL ON ω₁ AND DIAMONDS ⋮ The Cardinality of Reduced Power Set Algebras ⋮ Stationary cardinals ⋮ Some properties of \(\kappa\)-complete ideals defined in terms of infinite games ⋮ Some partition relations for ideals on \(P_{\kappa}\lambda\)

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